"Now if I lived in a socialized health care country I might be ok with that"
I don't think you'd find that people with universal health care are any more accepting of mandated tests or any such thing as those in the US. In fact, there is a national health service in Britain, but no requirement to have vaccs to enter school or anything else. Of course, doctors put pressure on parents to have vaccs, and are paid accordingly, but if you say no, your decision is far more respected than in the USA.
I think that the acceptance of mandated tests is individual to the culture and then the individual. The issue of socialized health care is irrelevant. You pay for the health care through your taxes, and it's still your body to make decisions about. It doesn't then belong to the government, and nobody there has that mindset.
Anyway, back to my previous post, I personally see the availability of such tests as a positive. But then, I've had a child with a disorder identifiied through those tests. I don't think any parent who has had that shock, and dealt with the subsequent issues, would disagree.
When you've been there, you understand.