Let's look the other direction: Humans come into contact with alien beings.
For ease on the mind, I'll make the aliens relatively humanoid. Let's say they have to arms, two legs, one head, two eyes, so on and so forth. They're in largely different proportions though. The alien head is large compared to their body, as their brain doesn't fold as much. Their gut is also long and they have higher blood pressure since they come from a high-gravity environment and their brains are so abnormaly large. They also come from a planet high in Chlorine, so though they still breathe Oxygen, they need Chlorine for some metabolic processes and can't really share food with humans. This also means we don't have to deal with bacteria transferral for a little while, which is good for our relations.
Let's also say that the Kirk method won't work. They lay eggs. While it's almost a certainty someone will develop or already has a fetish for that, randomly abducting and sleeping with the aliens isn't an option. They also pupate, and their larval form is maggot-like, turning people off a little.
Since we meet the aliens, we likely afre colonizing the planet. Let's say the alien life (Call them Xax) have spread across one landmass but a lack of a landbridge means that the "America" of their planet is devoid of Xax. We happen to land in "Eurasia", and we have just enough time to begin a small operations on the planets surface before we realize that we have a sapient life-form nearby.
Biologists are going to utterly flip their everlasting shit at this point. The minute someone realizes that these things might be sentient, he's telling everyone he knows, everyone he can grab onto for more than five seconds, everything he can get his hands on, his vaccuum, whatever. People will FLIP THE FUCK OUT.
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After enough people have heard the news, society is going to be in a uproar. At this point, no-one serious is going to be such a huge asshole that genocide will be suggested. There'll be our WBC of the future, but they shouldn't be a major opinion right about now. Right now, everyone is going to be working on polishing our collective boots and trying to figure out their language.
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But before we figure out their language, someone is going to, be it purposeful or accidental, alert the aliens to our existance, if they havn't been alerted already. They will probably see us as Gods, unless they've gone through their enlightenment, in which case they'll still act as if we're gods, although they won't belive us to be above reproach. It is at this point we can judge how far along they are from a non-material view; have they embraced reason over superstition? Probably not. If we had a chance of not finding them before we even shot the rocket, they're pre-radio, and probably pre-enlightenment. At this point, they'll freak out, and could do anything from create idols to conspiracy theories, to trying to murder us and offset the apocolypse. This should give us a glimpse into their culture. Let's asssume for the moment that they're peaceful and technologically dumb, but relatively quick to learn and quick to absorb new cultures. This is important, since this effects humanities opinion on whether or not we should genocide them.
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Capping off phase one, we get a small grasp on their language, in whatever form, and we can begin to converse with them. Since they're not very advanced, beaming them mathematics with lazors isn't viable, so we have to have linguists working overtime just to translate a scarce few words. But this opens new doors, and we begin to familiarize ourselves with the aliens. Humans are amazingly empathetic, at least on a individual scale, and we start to grow close to the aliens. Embassies are formed, and tech diffusion begins among the aliens.
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For the next few months things go smoothly, with the aliens learning our language and us theirs, and several biologists begin to develop close relations with the aliens. Video is streamed back to Earth, and people who have never been in contact with the aliens sees the biologists growing close. Humanity is naturally somewhat xenophobic, a direct opposite of our empathy, and some people begin to fear the aliens, thinking they are growing to close to us and are trying to subvert us somewhow. This fear has the curious side-effect of ending all racism and sexism; it's less important that she's a balck woman as long as she's human. Some people begin to seriously protest policies that are "pro-alien" and advocate the termination of contact with the aliens. In response, other groups arise, ranging from the isolationists to the xenophobes to the xenophiles, who are actually more sympathetic with the aliens than with their own species. If the world is still devided, wars will break out between nations, with differing ideologies depending on how their culture deals with new cultures. Religion continues to also play a part; radicals will be at odds with weekend worshippers and secular theists, some believing that the aliens were not saved or cannot be saved, some believing that the aliens are sinless since Adam and Eve were human, with the majority of people feeling divided and simply following what their pastor tells them. More xenophobic areas, like north korea and the southern U.S will likely be at odds with more tolerant areas such as Japan and the EU.
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The chaos at home will likely lead to chaos abroad. This is likely the first experience the alien Xax will have with the violence of humanity, and they will be frightened. It's quite possible, even likely, that they will become isolationist and afraid, and it's possible they may become responsible for some murders or an outright war. Humans won't as a group see the aliens as differing tribes, so the less violent aliens will be lumped in with the "warlike" ones and could become stigmatized. However, there will be a small but significant faction which perpetuates our ties and prevents a full on genocide. Relations persist, quite strained.
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Horrific acts are perpetrated by scared humans, possibly acting on offical orders from home. Eggs are smashed, and the time is recorded in history as one of the darkest moments in human history. Many people are horrified, and the pro-alien faction grows immensely. Relations are strained to the breaking point, but humanity has begun it's turn towards the positive. Opinion f aliens by humans is becoming generally favorable or neutral. Opinion of the aliens toward humans will be considerably worse, the memory of the horrors fresh in their minds.
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Peaceful groups begin to patch relations with the aliens, and their opinion begins to improve. Speciesism is still rampant, but it is no longer a majority opinion. Tech diffusion begins again, and the alien Quality of life improves drastically. With the improved technology rate, they may no longer see us as gods, and begin to regard us as falliable beings, albeit ones that are incredibly powerful. We're feared but respected amongst the alien community. A alien Anti-human faction may emerge now or in any of the closest three steps.
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The aliens are now close enough technologically and philosphically that they can be successfully integrated into society. Segregation is likely at this stage, in fact almost certain, though it may not be made into law. the aliens form neighborhoods in the midst of human cities and partake in human comforts. New commodities arrive as it becomes lucrative to make alien-fit clothing and alien appliances. Since these aliens lay eggs, human-run communal hatching centers begin to be founded, as we outgrow our disgust at their grubs. We interact with their children and our children interact with theirs. This generation marks a powerful downswing in the power of speciesist groups, and their political clout falls accordingly.
===> Alien life is now completely integrated into human society. Anti segregation groups push through legislation to finally give the aliens equal rights, and there is a renaissance of harmony and love as the power of speciesist groups falls to its lowest point. The new generation arises fuly integrated and anti-alien sentiment is regarded as old fashioned and outdated. Xenophilia is the name of the game, with aliens fully embracing human culture and humans fully embracing alien culture. This grows to a almost comical point before it starts to swing the other direction. Jokes that would have been considered offensive before are freely told by both sides, and nobody really cares.
===> The two groups begin to reseparate themselves. Aliens begin to act more like aliens and humans more human. The two groups are still integrated, but now they segregate slightly, regaining some old identity. While speciesist groups regain power or reform, they never grow beyond a few backwater citizens and asshats. The two groups of completely different beings are now completely comfortable around each other, and the integration is complete. Being an alien is no longer stigmatized or seen as cool in any way; it's simply a fact, like having a big nose. It's possible this stage or the last may not come without the intervention of a new species, restarting the cycle to be repeat.
tl;dr : The aliens almost cause a civil war/ do cause a civil war but eventually are integrated fully into society. Some amount of segregation would be completely natural. Even discouting physical differences, there'd still be a culture gap and people are just happier around people they're like. This can be seen today in schools. Generally, the races will separate themselves without any prodding. There is a significant amount of drift, but usually a table of children will be 90% one race or culture. This will probably happen just as naturally but more pronounced with the aliens. After we get over our inital fetish for them, they'll be too different. and most of the humans will have mostly human friends and the aliens mostly alien friends. I think that most of The world has reached Phase three with Blacks (for example), as an example of a inter-species First Contact. For aliens I think it'll be similar but more pronounced. Something to note is that a few things can be surmised:
>The propogation of a species means that the death of a "important being" will be seen as a murder. For humans, any countryman is a Important Being. For a hypothetical race of hiveminds, such as OSC's Formics, the Important Being would be a Queen, or perhaps several hundred drones.
>Violence will be understood. It may be seen as sexual, if the alien is odd or starfish-like, but it will probably be seen similar to how we see it. It will, after all, mark the end of one being, likey an Important Being, and the chances of a alien reproducing by dismemberment is unlikely simply by volume of all other means of reproduction.
>Viruses will have difficulty transferring over, due to their close relationship with the cells they effect. Bacteria, on the other hand, don't need the biology to be similar, but only to have a certain chemical for them to eat, and for their waste to be toxic to the host. This means a bacterial infection will be far more likely than a viral one, although it may not be possible either way depending on how different they are from us.
>If the species breathes an atmosphere entirely different from ours, integration will be much more difficult for obvious reasons. It is possible though; look to the Grunts from Halo as a effective way of integrating Methane breathers into a oxygen-breather environment
>The biggest issue won't be biological in nature. This may sound odd to you, but regardless of how many tentacle dicks it uses to eat it's food of jellied squirrel, the biggest issue will be the culture that evolves around it. Culture is far more differentiated from environment and it'll be much harder to guess what offends them and what doesn't. Imagine if the first westerner to meet with Japan walked into a house with his shoes on, rummaged through the fridge, and littered plastic down through the driveway. That would be far more likely to spark hatred than "he's so pale and his eyes are huge".
>Exercises like this one are just that; exercises. They can no more prepare us for meeting an alien race than running around the block can prepare you for a five-mile hike. It'll be better if we do do it, but we can't expect it to guide us completely.
>Finally, we have experience now with integration, and hopefuly the whole process of going from xenophobia to xenophilia and to the middle road won't take more than a few generations. In this case, the aliens will be reactive, and our moves will determine theirs. This is the only thing we can be sure of. Period.