People who would persecute others based on their sex and sexuality are also likely to be GC
Not as I understand "gender critical", they aren't. Anyone who wants to persecute others based on their sexuality is likely to want to enforce gender stereotypes and social expectations. Being gender critical means rejecting gender stereotypes for everyone. Everyone can wear what they want, have whatever interests they want, date who they want.
People who persecute others based on their sexuality are likely to be conservatives. They are people who want to enforce gender roles and stereotypes based on sex. This was neatly conveyed by that Venn diagram which did the rounds some years ago: