No. Gay stuff was largely people just growing apathetic to something not integral to them or their beliefs. Troon stuff, anytime it appears in public, is roundly rejected if dealing in any way with kids and even the general acceptance is seeing sharp declines in acceptance. Your foundational premise is broken.
Carter's greatest flaw wasn't a lack of intelligence, or a lack of courage, or any lack of personal character. it was in fact the opposite. He was unable to dirty himself enough to actually do the job.
He'd have made a really good VP in the same vein as Pence. By this, I mean the wingman to someone more bombastic and willing to play dirty. Trump used Pence to great effect in that role, and Carter would have been superior in that regard.
But not as President.