Don’t have a problem with:
A main character who’s explicitly wicked, shady, criminal, or morally compromised. Grand Theft Auto, Mafia, Saints Row, Hitman. It’s an old trope (I think the PS2/XBox era is when it really took off) and from a moral perspective no different from accepting a villain role in a movie. It’s fun to play the bad guy!
Doing unethical things that the game is designed to reward. My go-to example for this is Dynasty Warriors 5 Empires, where you can either go for Good Emperor (which takes absolutely forever and costs you astronomical amounts of cash and troops, for the benefit of some feeble peasants fighting by your side), go for Evil Emperor (which nets you tremendous…and UNLIMITED…amounts of cash, goods, and troops, at the expense of a bunch of hapless peasants opposing you on the battlefield), or remain dead-center neutral and be content with King. The only time I took the good path was to unlock the ending. Evil was just overwhelmingly better (and neutrality had an appeal of its own).
Doing wild, wacky, or dangerous things that would be a bad idea in real life. Terrorizing pedestrians in Crazy Taxi. Damaging public property in Tony Hawk’s Pro Skater. Taking all kinds of dubious smash and/or grab missions in River City Girls. Fun! As long as you can separate fantasy from reality, no harm done.
Taking dishonest or unfair actions that are incorporated into the game mechanics and fully intended to be exploited to the full. Blood Bowl could not exist without all the fireballs and lightning bolts, illegal weapons, illegal magical tools, cheap shots, ref bribes, one-off mercenary signups, constantly interfering fans, and on, and on. It’s cheap, cruel, nasty, vicious, and intensely provocative, and that’s what makes it so awesome.
Being able to take truly reprehensible actions, but only with serious consequences (up to and including making the game unwinnable). It’s a very old example, but I recall Pool of Radiance skillfully incorporating these. You’d better not lie to the undead priest about Phlan being free, you’d better not kill the helpless fortune teller living alone with no one to hear her dying screams, and you’d definitely better not raise a blade against the good, honorable protectors of civilization.
Have an enormously massive problem with: Presenting an execrable worldview as normal or even admirable, particularly from the perspective of the main character. I again turn to this bitter journey. Supporting a sadistic butcher and a blood-crazed war dog to the very end, quietly accepting the clan leader’s horrible judgment, condemning a valiant and completely innocent man to die alone and forgotten, doing nothing about the continual acts of injustice and butchery done to those around her, and on occasion herself…Eivor is the absolute antithesis of who I want to be the hero. The worst part is that the overriding justification for all these atrocities is respect for authority, tradition, and structure, which is just daft if you know anything about, oh, pretty much any other AC protagonist ever. (Not to mention the little issue of all the slaves she absolutely had to have gets completely glossed over…I know it wasn’t a bunch of rowdy raiders building all those structures and doing all the work needed to keep the community functional.) She’s a better Templar than any of those Order of the Ancients schulbs could ever be!