This is a straight question, please don't take it in a sarcastic sense.
Now, my premise might be wrong, but assuming an Atheist does not believe in an afterlife or even more basic, some sort of cosmic balance (a la Hinduism or Buddhism, among others), how do they reconcile (or even rationalize) the vast difference in standards of living between people in the world (especially in the western world, whose standard of living is vastly superior to rest)?
It really sucks. And as you point out, we don't believe that it's going to be rectified after death. If the problems are going to be fixed, we have to do it ourselves, here and now. Fortunately, almost all humans have compassion, so we feel the urge to help to some extent.
It's actually stranger that religions encourage charity, while at the same time saying that the downtrodden will be rewarded in the next life. It's a bit inconsistent, but it makes sense in the context of seeking converts. Religious charity almost always involves evangelism, a very effective combination. The unfortunate person is offered food now, and a palace in heaven later. The missionary feels like a good person because they're being charitable. Everybody wins, especially the religion's population number.
The thing is, charity isn't a religious thing. Everybody has an impulse for charity, that's the reason charitable missionaries feel good. The reason religious groups are able to spend so much money on charity, besides being massive, ancient organizations, is that it's also their recruitment budget.
But atheists don't have this, so how do they manage the dissonance? Or do they not just think about it?
This is not to say there aren't charitable atheists (obviously there are) or uncharitable theists (unfortunately), but in the latter case it would be considered a sin and some sort of guilt associated with it, whereas in uncharitable atheists, my question is whether a similar guilt is felt, and if so how is it resolved?
Definitely. And my opinion is that that "guilt" is behind all charity, but religions piggyback on it to gain converts.
And to be fair, all sorts of other groups attach their agendas to charity also. Particularly governments or political groups. But my point is that compassion is human, and certain groups just take credit for it. Resulting in people wondering why nonbelievers would ever be compassionate... As if we're all sociopaths. Which is silly because we're not the ones being coerced to do good by religious doctrines.
The sad thing is that a lot of religious people seem to think they would be evil, if religion wasn't forcing them to do good
I don't believe that. It's a false teaching which keeps people in line.