"My kid being sick" is not a standard by which others need to operate, and in fact, sometimes - SOMETIMES - it's the others who have the cooler head and the broader vision to maintain perspective.
Question to you .... if the reason my kid is sick is directly BECAUSE of the way that others operate, does that change your stance. Alternatively, let's replace "sick" with "bullied"... does the same perspective or standard apply?
I'm not sure EXACTLY what the question is, but even so, it depends. For me - and I don't mean "my opinion", but rather, my knowledge of the law and concept of forcing behavior of others - the key words are "directly because". Some yahoo in Missouri not getting the vaccine is not "direct cause" to my kid having COVID in the same way that, say, running over them with a car would be. Even if some yahoo in Hartford, CT doesn't get the vaccine, and there's COVID in my school, it's not a "directly because", since we KNOW that you can get COVID with the vaccine and many vaccinated are asymptomatic (statistics don't matter here, so don't reply "but the ODDS!"; we're talking direct causation not probabilities).
Same with bullying; if Kid A (haha, I hate Radiohead!) comes up and punched my kid in the balls and takes his lunch money, then Kid A ought to be punished. Do I necessarily think that all other kids now have to act a certain way because my kid took one in the pouch? No.
If you're talking something more general, like car seat safety, or, I don't know, child predator laws, there are mechanisms. If you think someone made your kid sick, sue them and see if it pans out. I can't speak where you live, but there are easily a half dozen lawyers in my neck of the woods that would take the case on contingency if they thought you were right (John Haymond, Carter Mario, Mark A. Salomone, Trantolo & Trantolo, Gould Injury Law... I can sing the jingles if you want!). We're really talking about forcing someone else to act proactively on the OFF CHANCE that your (or someone else's kid) MIGHT get sick.
And INB4,YES, I know this is how we - really, politicians - operate, and that doesn't make it right. That we consistently close the barn door after the cow gets out doesn't mean it's a great strategy. I give the example all the time: Chris Murphy crying crocodile tears while pandering for votes with his arms around the families of Sandy Hook, while they stand there in shock like deer in headlights.