Eh, in my experience the people arguing for female space marines tend to be the types that think that the Imperium is emphatically the good guys, they literally want diverse oppressors because they think that when women do it, it's not oppression.
That has not been my experience at all. The key difference between FSM and "More lady drone pilots flying rainbow drones!" is that one of these.is a game that we want everyone to play. We do unironically want more ladies to feel comfortable playing the oppressors because it's a game and the space should feel inviting to people generally.
Other miniatures games (Infinity etc) have near-parity in male and female sculpts and don't have massively more female players playing them. Female warhammer players generally don't feel comfortable with the militarized aesthetic of Space Marines, regardless of whether the person inside the power armor is a woman or not. To make them more comfortable in the hobby, focus more on Tyranids, Eldar, and demons.
The majority of the FSM crowd is men uncomfortable with their maleness, however, and that needs to be addressed.
Again, not in my experience. I don't know which of our experiences is more common, but it'd be interesting to see some data. Though more focus on non-SpaceMarines can only be good for the hobby.
I can't speak for more female minis, since giant robots don't have genders generally, BUT my first interaction with Battletech wasn't about a conglomeration all-male posterboy factions that comprise fully half the game and have their own prequel game with even more All-Man Space Marines.