It's an interesting starting point OP, I get what you're saying, although I can't say I've experienced anything similar.
I have an older sister and I'm my mother's favourite, not fair but true, sadly. It damaged our relationship until recently. Our father treated us equally but my sister held our parents at a distance and so I've grown up closer to my parents, to the point that my sister wouldn't spend family holidays with us in her mid-teens.
I have one son, he will be an only child. He is being raised to view men and women as equal partners who both work and share in running the home and we each spend equal time with him playing, if anything his Dad is more involved at the moment as our son isn't in child care.
I challenge every tiny little bit of gender stereotyping that pops up, he has recently rejected playing with his friends who are girls but we go on play dates with them anyway. I don't think I ask him to talk about his feelings any more than I would a daughter but I hope to maintain a strong, close relationship with him as he grows into a man, which is a long way off tbf.
It's probably a coincidence that the friends who have rejected you might be mothers of boys and so come from a different perspective 'my son is lovely, not all men are rapists' or something like that (on the false accusations point) but it's become confused with something around wanting to protect daughters from men. I make no excuses for them, they don't sound like very nice people to have dropped you for holding that view.
I hope this helps, you sound like you have a lot going on in your head so hopefully this is helping to clear it a bit xx