Women do these to men, too.
I agree with your post that it’s bothersome to feel obligated to accept gestures you don’t feel are genuine, but you’re villainizing a group based on their gender. Don’t think you’re exclusive to being thought of as inferior or as an object. Men are frequently thought of as inferior and are very frequently objectified. Call me biased, but emotionally, the damage is real for whoever is targeted. Because one group does it does not make it right for the other.
Some men are sexist and so are some women. One gender might represent a larger portion of the injured but that doesn’t mean that gender should attack the other as a whole. The injured should stand against the attackers, recognizing that the injuring is what’s wrong, not the gender. I want to believe you know this already and that you’re pushing for a greater cause of equality, not just an anti-man world.
Equality has improved with addressing individual’s flaws. People on both sides will always fall short though. But they’re just people. Let’s not push against the shape or sex of the human, but the acts of individuals as individuals.
Men aren’t bad. Women aren’t bad. We’re all people, and we really would be smart to treat each other like people.