I did not find Corden to be stereotypical (well, not beyond what is explicitly written into the script) or necessarily offensive in his depiction of a gay man. I don't mind mincing and flitting and flaming and queening out- I do all those things and so do all of my friends. I just didn't think he was particularly *good* in the role- he's somewhat miscast and not particularly ever convincing. He's... inauthentic.
I do think casting a straight actor to play a character like this- whose whole story is that he is long estranged from his parents and had been denied a major moment of teenage years, due to his sexuality- in 2020 is tone deaf, and undercuts the message of the film.
Have straight men given good, even great, performances as gay characters? Absolutely. Robin Williams in The Birdcage or Jeffrey Wright in Angels in America immediately come to mind. But again, those are now decades old, and there were substantially fewer openly queer actors in Hollywood. Times have changed.
Something that stuck with me was a comment that Murphy made in the conversation that follows the film in the press screener version: he says he wanted to make a movie he would have wanted to see when he was growing up. Which is understandable! But it's also 2020 and he is separated from the world of his adolescence by 40+ years.
"...everyone finally shut up, and the audience could enjoy the beginning of the Anatevka Pogram in peace."