Um, yes, treating them as not women in things that matter to them, like what bathroom they get to use, is important. Registering for a draft that is never going to happen is not.
I would have no problem with having women register for selective service, since they can currently serve in nearly all MOS roles in the military.
But the thing is, we don't currently have a draft. We are not going to start a draft. If we do start a draft, we'd have to make decisions on who to draft, and as it stands now, 71% of eligible cis-gendered males wouldn't qualify due to past drug use, obesity, lack of education, etc.
About 75 percent of US 17- to 24-year-olds are ineligible for the military due to lack of education, obesity, physical problems or criminal history.
www.thoughtco.com
As someone who served as an NCO in the Army, I certainly wouldn't want to train draftees. It was hard enough training people who actually wanted to be there.