You will alienate the masses if you perform any crime in front of a moderate/liberal. The one exception to this is attacking conservatives, but note that there's a chance that you'll miss and hit an innocent if you do this. It's probably better to try and avoid fighting when moderates/liberals are around, yeah (if you're about to initiate combat then you can talk to them to make them go away).
Actually some crimes are OK to commit in front of Liberals and/or moderates. If I recall correctly, stealing loot off the ground is something Liberals don't care about (since they don't respect the idea of private property) but if you do it in front of moderates you Alienate The Masses which is bad but not quite as bad as Alienating Everybody.
It's true that if you fight Conservatives, this won't get the Liberals or moderates upset with you. But the risk is, you have a 1% chance, with every attack, of accidentally attacking someone who isn't the enemy, if there are Liberals and/or moderates there as encounters (rather than members of your squad). 1% is a very low chance, yes. But let's say you have 6 people in your squad, and you fight people again and again and again, and the people you fight are weak, and you get 1-hit kills on all of them. Pretty soon, statistically, your chance of accidentally attacking a Liberal or moderate that you encounter, when there is also at least one Conservative encounter too, starts to grow exponentially before it ends up asymptotically approaching a limit of 100%, and if you do a massive amount of fighting at the site against groups of encounters that have mixed political affiliation, the probability of attacking a non-Conservative by mistake is very close to its asymptotic limit of 100%.
And if you hit a moderate you'll Alienate The Masses and if you hit a Liberal you'll Alienate Everybody. Not good.
What this means is, you oughta have Stealth, and wear something that gives you good Stealth and also good protection from being hit... i.e., the SEAL Stealth Armor also known as the SEAL Suit. Then avoid fighting mixed groups that have any moderates or Liberals in them and only fight groups that are all-Conservative. I go further and avoid fighting anyone except 1 Conservative by themselves, because if there are multiple Conservatives, they might be able to get some damage in on me before I kill them. Of course if my safehouse gets raided, I'm unable to do this strategy of fighting 1 Conservative by themselves, since they'll always appear in groups of 6. But if the safehouse has traps, a lot of those Conservatives are already injured before I fight them, and so they are easier to kill. So make sure you have traps at your safehouses (both booby traps and tank traps). I typically go for all the safehouse upgrades except the AA Gun since it's too expensive and I never actually get the type of raid where I need it. Well OK I USUALLY don't, only sometimes. Sometimes if I've committed "Treason" (ridiculous, since I hardly think what I did was treasonous, it was just publishing some controversial documents that the public had a right to know about) they come after me with bomber planes and bomb the LCS safehouse with the printing press that published those leaked documents in the Liberal Guardian. That's hardly a proper reaction to my legitimate journalistic enterprise, but what else would I expect from the Arch-Conservative military-industrial complex? I guess my point is, it's probably best to get ALL the safehouse upgrades, even the super-expensive AA Gun, because you just might need it... although to be honest I don't recall Glenn Greenwald ever having a U.S. bomber plane kill him for publishing documents that were leaked to him, here in the real world, nor did a U.S. bomber plane kill the guy who leaked the documents, Edward Snowden, either. Then again, we are doing those drone strikes against thousands of people deemed enemies of our nation... I bet if the siege on the Branch Davidian compound in Waco, Texas happened today they'd use drones to attack it. That siege is probably the closest real-life analogue to the sieges in Liberal Crime Squad, except for the fact that the Branch Davidians weren't exactly liberals.