Selective Service and being transgender

I need some advice. I was born female, transitioned to male 20 years ago in my late 20s. Got all my documents changed, and noticed hey I'm over 25, I don't have to register for Selective Service. Cool. Now in my late 40s, I find myself working for the federal govt. Uh oh.

I have, as of now, been a fed for almost three years. I have so far had the initial employment background check, plus two more along the way to get access to stuff I needed. Each time someone's been like hey so why didn't you register? I'd explain and they'd be like oh okay no big deal. I'd prefer not to have to keep telling people I'm transgender at this point in my life but I have to explain why somehow. I'm not sure how to tell if I'm enrolled in the continuous vetting but I probably am.

So here's my current dilemma: it looks on the website like I could register now. That would eliminate the questions about why I never did every time I need a check or get a new position etc. But it might also paint a target on my back, which under the current admin I'd really rather not do. I mean my passport and SSN list me as male and presumably those systems would show there was a change back in the late aughts. But those changes were ages ago and I kinda feel like someone would have to go looking for them.. where registering now might bring that to the forefront?