The crux of the disagreement is whether--given this very real betrayal by the left--the answer is to join w/ the right. Setting aside everything else, cleaving to orgs like Family Policy & Heritage further the (wrong) impression that only the far right cares about the issue.
Really, the ppl you most need to convince of your approach are those wary detransitioners who've made it quite clear they won't trust these orgs. They are the people who've been harmed and have standing to say so (including in a court of law).