I would refuse to move seats if asked to do so by a haredi or other religiously motivated man. I would politely ask the aircraft staff to move the other passenger.
I would happily swap with DH so that an unaccompanied minor could sit down. DH is also no threat to anyone, but he understands that it is not about him.
Many years ago, DH and I flew to Ireland together in August. For locals, it was quite warm, and they were all in shorts and T-shirts. But we had just come from a 42-degree heatwave in Greece (DH is Greek), and DH was freezing in Ireland. He was wearing a heavy jacket, and it must have looked suspicious, as it was full of odd bulges (presents for people stuffed into pockets!). When we landed in Dublin, he was the only person in a coat, and when we queued at the passport gates, he was pulled out of line by security and thoroughly checked. He was not offended. He did not accuse them of racism or anti-male bias, or anything else. Mature adults understand that it is not about them individually, and that safety procedures are there for a reason.