I mean, again, even in the 21st century you can't force your relatives to get treatment unless you're their parent.
There are major differences between the 21st century and the 24th though.
For one thing, since there is no money when the UFP formed, medical care is free and accessible to everyone (not to mention the fact there are practically no waiting times and body scans are very quickly done with scanners).
Second, everyone would be exposed to relevant general education, critical thinking and problem solving (in fact, given the kind of radical socio-economic shift Earth went through after WWIII (eliminating poverty, wars, disease, etc. - I suspect many things like medical care and basic necessities were accessible to everyone even at this stage - aka, during ENT run - and once again when UFP was established) you wouldn't expect of these people to develop anti-tech sentiments to begin with - or if some have, they wouldn't aschew ALL technology and science... but mainly restrict stuff they deem to 'rob them of joys of living' (as they explain it).
But from what I can tell, the Picard's weren't originally that anti-tech. They had modern technology and we saw Jean Luc using pads as a kid after all. So, not complete Luddites or anti-tech environment (they also had lights, electricity, etc. - I mean, those are an extension of technology after all, so even the house itself would be considered 'technology').
It seems more anti-tech views developed in Maurice (and Robert) after his wife died... prior to that he may have been more open and only limited certain tech as he didn't seem to find it particularly useful for him or took something away from him.
Later on he may have developed more stringent views of limiting use of most technology 'that made life too easy or robbed a person of certain things' (in his view).
Also, I don't think anyone in the UFP would force people to take medical treatment... there would be no need to because the majority are educated to understand the importance of frequent medical checkups (and its accessible to anyone who needs it)... in fact, I wouldn't be surprised if people go do medical checkups every few years or so (given the state of medicine in general and preventative measures taken early on, serious issues would be happening infrequently which would reduce the need for visits to the doctor).
In space (when serving on a ship), things are different. Some times people can go for weekly checkups, but it seems most of the time, people do monthly checkups... or a few times a year (barring any issues).
I suspect checkups might be a bit more frequent after away missions, but would soon go back to routine (but that's space).