During Vietnam there was a rumbling about drafting nurse (female). At the time the number of male nurses was much smaller than today, and the need was outstripping volunteering. Now slightly more than 50% of the medical students are women, so if we have a "doctor draft" it will have to include women, for both practical reasons and the legal issues noted above.
In terms of women in combat arms, basically infantry and artillery and to some extent armor, the question is physical capability. At the end of the day you can only reduce the load a grunt carries so much, and if you are a 110 pound woman versus a 175 pound man the 70+ pound load is a good deal more strain. This does not mean women cannot be in these branches, it just means that a smaller percentage of women can do this compared to men. This even apples to things like corpsmen/medics with combat units etc - they have to be in the same physical capability bucket as the riflemen. You can move women up closer, communicators in a battalion HQ,etc.
Doing all of this in 1900 is ASB or requires a POD way back in time. Having this happen sooner than OTL would require, as somebody said, an existential threat to the USA that required this sort of manpower, and even then it would start more "Rosier the Riveter" than women in combat branches. IMHO if the USA ever reinstituted a draft you would see women register and be drafted, albeit with more outs like you see in Israel, and also you would see assignment to combat arms NOT being only voluntary. Not a ton of women grunts, but there would be some and some of them would not have been ones who raised their hand.