The case with minorities/LGBT wasn't to do with respect for body autonomy, it was due to not viewing them as counting as 'people' in the first place. Even if they believed in complete bodily automation, I don't think it would have been applied there since they probably wouldn't have viewed that right as counting in the first place.
There's a clear line of difference that can be drawn between 'vaccinations' and 'forced sterilisation' so I don't think equating them as one-opening-the-door-to-the other is in itself a useful concern. Though there are definitely certain powers I think should be excluded from the state on principle, being able to execute your own citizens for example, but 'complete bodily autonomy' isn't one I count as a current core principle any more than 'complete financial autonomy' (since taxes exist, the state has a right to some of your money). The state already has a claim to your body, the argument is just in how much.
Heck, if given a referendum on the subject I'd vote to remove the ability for people to opt-out of organ donation so that may indicate where on that line I fall anyway. But I'd also decriminalise the taking of illegal drugs, but that's less "The state has no right to tell you what you can and can't put in your body" and more "Criminlising addicts doesn't really help the addicts" and "Some illegal drugs just aren't illegal for a good reason anyway".
The USA system of checks/balances is also one I find a bit weird to be honest, being based more around pitting 3 branches of government in direct opposition to each other and hoping that none of them ever 'win' the resulting conflict rather than setting up actually independent bodies of oversight. It's closer to the Holy Roman Empire Pope/Emporer structure, where Pope could crown Emporer could install Bishops could select Pope, and that didn't work very well then either.
There are a few USA systems that at a glance almost seem like they were based on a misunderstanding of older systems, like how the USA president has legal powers comparable to those of the British monarch but without the centuries of tradition/president that made them never actually get used even back when the presidency was founded. In practice the British monarch can't actually use their power of veto, whilst the US precident can and does.