The thing about cops is that they enforce the law. That's their job. I've seen it more than a few times where the player doesn't let go of this to enjoy the rest of the game. These people are like the vampires who call for torpor because someone dissed them slightly. It's not fun.
Also not fun is getting in a situation where you can't do something because one side or the other is decrying how It isn't fun for them. Well now nobody is having fun.
I don't mean to not pick on the criminal characters, because this kind of person lives everywhere, but we have a far better vocabulary to say which criminal tropes are antagonistic, and we are otherwise okay with the music pirates and prostitutes, and sometimes even the mafia and tong characters.
But here's the thing about police: Their job is to stop things from happening. I thank many of them for being in the line of fire and doing some very hard shit, but in the broader perspective, on a role playing game about the dark horrors of our world where we're playing monsters, the cop is the antagonist. Not always, sure, but eventually it will be the morally questionable against the thin blue line.
Like any antagonist group, I'd be careful with who I'd let in, until we can rephrase their role on a game to something less absolute.