I don't think people should be forced to use public infrastructure and services, simply because tax whores won't allow competition.
How is that possible?
Easy, by not being an asshole, oh wait I forgot! That's too difficult for some people!
I mean, how is it possible for someone not to use any public services or infrastructure?
That is part of the problem. The "public services" are typically a monopoly - people are not allowed to opt out or are penalized if they do. Then the monopolists play the guilt card - you owe "society" because you used the service they coerced you into using. You used some of them - the neonatal hospital, for example - before you were even sentient.