I don't remember what's recommended if you change a state ID (drivers license and so forth) without changing your sex marker with the feds. But if you do change to M with the feds and you ever expect to work for the feds or get aid from them, you need a status letter from Selective Services. I recommend that you get one even if you have no plans involving the federal government because you never know when your life will take an unexpected turn.
A few years ago, I was unemployed and trying to get some job training from an agency whose funding source I never fully established, and the agency required that I furnish the letter. I did so, but they refused to proceed further until I told them about the nature of my dispensation. I said that I was exempted on medical grounds, but that wasn't enough to satisfy them. I was then told that the agency needed to know the EXACT nature of the exemption because the agency needed to establish that I hadn't committed any wrongdoing by not registering. I told them that the federal government itself had stated that I'd not been required to register, and that should be that.
That wasn't that, and I refused to out myself to this agency because they had already dissed one of my trans brothers the year before. So I got no job training. I thought they had a lot of damned nerve, deciding that their evaluation of my SSS situation should supersede that of the federal government's. So I gave them the figurative middle finger. Boy, was I mad.