"Since now everyone is paying for each other's health, that may give people a "right" to say I can't smoke, I can't ride a bike without a helmet, I can't eat trans fats"
You do realize that private insurance companies have been headed in that direction (enforced by varying premiums) for many years already, right? And this legislation actually puts limits on their ability to do so. (They can still price-discriminate on a few things, including smoking, but only up to a prescribed limit.)
"is anyone worried that these sorts of things may become legislated (more than they might be already)?"
I'm not. I've seen no examples of that sort of over-reaching law WRT medicare or medicaid, which are certainly impacted by personal health/lifestyle choices. If you have an example of it from, say, Europe or Canada (both of which subsidize health care to a greater degree than what this bill is doing), I'd like to hear the details.
"Is it wrong to want to keep certain medical issues out of the hands of certain medical professionals?"
I don't know about "wrong", but it's certainly foolish. Get doctors you can trust, and give them the information they need to do their job. Deciding that you don't think they need to know such-and-such doesn't make a lot of sense. They've been to med school, so you might want to let them decide what medical information is relevant.