I know little about Anthony Burch myself other than what others have spoken about, but the crux of the arguments seems to be that his apparently willingness to deliberately inject his own views in to his work for the sake of the story is what causes people to be concerned.
My take on such a view is that every aspect of a story should exist for the purpose of furthering that story, and if it doesn't make sense to include either don't include it or find a way in which it can work while not taking away from the narrative. Do what you want just make it make sense and don't brute force the idea. That's just my take and I'm barely a hobbyist writer myself so I can't speak to practical experience, only personal opinions.
If this fellow is working at Riot then he will not be working in a vacuum and Riot's already talked about, in regards to story, not including stuff just for the sake of including it. That's one big reason why so many characters have unconfirmed sexual interests; it's not relevant and only will be if the needs of the story make it so. For this reason I don't see a reason to worry as he'll be working as part of a team and while he'll have influence he's also as part of a collaboration rather than a solo effort. He'll also likely be working under folks so he'll have higher ups to answer to.
TL;DR While what I've heard about his decisions in story telling aren't things I'll necessarily agree with, I'm not concerned that him being a Rioter will be a detriment to the lore because of the environment he'll be working in.