What if accusation is proven (and this person agrees with it) but said person does eir work really good. Should ey be forcefully removed from this position? What if there is no good replacement candidate at this time?
Your PS seems conceited to me. Singular "they" is how the community of English-speakers handles this; it harks back to at least Shakespeare. It's miles more "correct" than any weird neologisms.
p.s. pronouns used are from https://www.orionsarm.com/eg-article/495360fba7a46 , I don't think singular they is correct thing.