If the left is going to continue to embrace unpopular policies, of course conservatives will try to capitalize on it. They hand a bully a stick and say "please hit me with this stick" and are shocked when the bully hits them with the stick. And they do it over and over. Male people competing in women's sports is a very unpopular idea, but it's one of the first things Biden implemented when he took office. Medical gender intervention on prepubescent kids is an unpopular idea, but they picked a cabinet nominee who is an outspoken advocate for that, and are surprised that Republicans questioned her about it at her confirmation hearings. Of course they did. Why wouldn't they? It's free candy. Of course they'd take it. Stop giving them free candy. Stop handing them a stick and being surprised when they hit you with it.
Ah yes, just give the bully the lunch money and he won't hit you. I know you're not stupid, but this is very, very stupid. The right is gonna respond in bad faith regardless of how popular the policies being pushed by the left. Universal healthcare, green energy and student debt forgiveness enjoy widespread popular support, but Republicans will attack anyone who advocates for them as a communist. They will never, ever, ever respond in good faith and will always find a way to twist things into a culture war issue so the idea of appeasing them is for suckers like racist Bill Maher.
Now with all that being said, I also think the Democrats (who are not the left) use niche social issues as a way to district from their utter unwillingness and inability to do anything to improve the lives of the people they represent, including marginalized communities. I guarantee that transpeople in men's or women's sports is not even a top of mind issue in the trans community.They'd much rather have free healthcare.