And we can still root for them. What I find weird and uncomfortable, is that a lot of people seem to not want moral nuance or complexity.
They live complicated lives and sometimes want something simpler than exploring nuance and complexity to break with their regular complex and nuanced games. I mean, you can be the most deep philosopher in the world and sometimes enjoy an action hero movie, can't you? You can be the most lawful person in the world and enjoy a film where someone act as a vigilante sometimes? There is also a cathartic value: in real life, beheading your coworker when they irritate you is generally frowned upon, and acting it through roleplay, or seeing it in a theatre, helps one process natural feelings without enacting them in real life. So you behead a dragon instead, despite not applying all the possible ways of dealing peacefully with the situation. It doesn't mean people do not want moral nuance and complexity, it is that sometimes, they might want something else to complement their regular complex and nuanced game, where they ensure that the cattle raiders are given a fair trial when brought to justice in the cattle-owner village and will have long debate on whether they should defend these prisonners against the local population who want them hanged without considering that they let their cattle graze on the cattle raider ancestral and unmarked land.
They want to play characters who are objectively good,
Not necessarily. You can play people according to the morality of their character : if you're playing cultist of Aurile, you're content to have the people of Icewind Dale die of hunger and long for the rise of cannibalism among the local population, because, well, that's the will of the Goddess and it's right to serve her. You can play people who are objectively adept of a Blue and Orange morality, or roleplay a low moral scum (most Eberron characters with film noir inspiration, would fall into this category) or simply, like most real life human, unconcerned but happy to rationalize his actions as good. I haven't seen so many people wanting to play character who are objectively good. They mostly are good in setting, at best (ie, like you said, they'll be OK not to apply any sort of mercy to prisonners, saying "we didn't invent the Geneva Conventions yet").
but still do things that are from any even-semi realistic moral perspective rather questionable.
Semi-realistic moral perspective include real life moral perspective of people and civilization we would find morally corrupt by our standard. I'd say that they want to do thing that are "by our current moral perspective, rather questionable" would be a better way to formulate it. Elizabeth the First certainly had some degree of morality by which her acts were justified (and you'll probably find people nowadays to say she was a great queen), yet we wouldn't today accept her political, religious or colonial violence.
How about just play characters that are not morally perfect? Like not outright villains, but just people who feel anger and fear, experience realistic emotions and prejudices, that do not always do the right things? I have far less issue with a person who plays a vengeful barbarian that slaughters fleeing enemies in anger, with the player understanding that this is rather messed up thing to do, than a player who does the same but insists that their lawful good paladin was perfectly justified in doing that.
I have no issue with either. In both cases, they are understanding that they are playing a character: a fictional misguided barbarian slaughtering fleeing enemy in anger and thinks he's right because he's raised to despise cowards who flee, or who think he's wrong and acknowledge his flaws, or a fictional misguided paladin who think he's right because, basically, he think his god/the society he lived in told him he is. All are flawed by our standards (and we are flawed by other standards), some recognizing it or not, and their behaviour implies nothing on the player, who in both case is playing a character in a fictional world that operates by different values than our current values. If you're playing Horatius, can't you at the same time say that Horatius was perfectly justified in killing a Roman woman (his sister) for mourning the death of an enemy of the country, as demonstrated by the success of his (father's) appeal to the people of Rome, and understand that such behaviour would be unacceptable today?
I'd be more worried if a player truly believed his paladin character was good in real life and not just good in the flawed context of his surroundings.