It's mildly annoying, but does it BOTHER me?
Not at all. Virtually all of the constant moaning and bile about City is the same old fan tribalism thinly disguised as some kind of moral crusade.
Yeah, the UAE has a pretty bad human rights record in addition to building its wealth through polluting fuels. However, most of the screaming over this comes from supporters of other clubs whose owners aren't exactly paragons of morality, either. Kroenke came about as close as you can to literally throwing poor people out of their houses without actually showing up on their doorsteps. I can think of at least one owner here in the US that made their fortune through subprime loans. Chelsea are also a "petro club" due to Abramovich. Shinawatra was a thing here at City but nobody cared simply because we were still shit.
Bottom line is lots of owners across major sport, both in the UK and beyond, have gotten rich through less-than-admirable dealings. City being singled out by supporters of these same clubs reeks of hypocrisy, and in any event, what are we as supporters supposed to do? Switch teams? City were here long before the UAE takeover and City will be around long after they're gone. Any club is a hell of a lot bigger than whoever is paying the bills at the moment, just ask anyone who supports Hull or Blackburn.
The other big thing which City are criticised for are being "FFP cheats." Funny how although most fans are in universal agreement that UEFA is a corrupt, poorly run organization, but then City are implicated in an FFP case and miraculously, everyone is suddenly all about following the rules. The only joke bigger than the way rival supporters reacted to the FFP nonsense is the FFP scheme itself.
The FFP rules are completely harebrained in that they prevent investment the same way it works in basically every other business - put down some money and possibly be in the red for a bit until you start seeing returns. This is exactly what happened with City but the FFP rules somehow ignore this reality of the business world and attempt to drive a screw with a wrecking ball. I really can't be arsed either way as to whether City are flouting FFP, it's anti-competitive and has nothing to do with increasing parity on the pitch.
The clubs aren't responsible for "ruining football." City aren't, Chelsea aren't, even PSG aren't. If people really want something done about ultra-rich clubs buying any player they want, UEFA and the FA should step in and do something to try and restore competitive balance - of course, anything like an American-style salary cap would have people up in arms, but funnily enough, fans of other big clubs like United will yell about how it isn't fair to them to limit their spending because "they earned that money."
Earned how? The answer is TV revenue, which matters because old guard clubs like United and Liverpool have tons of gloryhunting fans that probably couldn't even find Manchester or Liverpool on a map. They rake it in from all the eyeballs they get from fans like these. I'd hardly say that's a respectable way to make money, and I've already gotten into the fact that tons of clubs have owners whose wealth is derived from questionable sources.
Nobody actually cares about all these alleged "bad things" City have done. It is tribalism, pure and simple. Don't let anyone convince you otherwise.