I kinda wonder if this move is being done with actually consulting with gender scholars on this, because yes, "man" can have that general sense like "mankind" to encompass an entire people; gender scholars would be the first to point it out. On the contrary, Marvel Studios has some history with overstepping/overcompensating and messing up anyway because while they tried to be conscious, they didn't ask the people at the center of that representation (e.g. using a lot of Asian imagery and themes without consulting Asian scholars led to some backlash for both Doctor Strange and Iron Fist, which in turn ensured that Marvel didn't repeat those same mistakes with Black Panther, and now Shang-Chi; Star Trek had a similar problem in consulting a white guy-masquerading-as-Native American, and not an expert of Native American descent, in creating Chakotay in Voyager).
This is likely my own bubble and changing the name of the X-Men to me isn't that big of a deal, but in feminist, LGBTQ, gender circles I've seen, I've never seen a complaint against the name X-Men from a gender standpoint, and moreso, the X-Men as a brand tends to resonate a lot with those circles because of common minority themes. Sure, "X-Women" has been used before, but that's more of a unique identifier within an entire brand and franchise.
My point being: I'd bet that if Marvel asked gender scholars and activists if they have a problem with the name "X-Men" from a gender standpoint, they'd not only say there's no problem with it, but that the name should be kept.