...snip...
Focusing on making every single person who does or who might consume or benefit from a service (particularly services where consumption can hardly be avoided) pay a mandatory fee for the service is likewise an archaic way to look at such issues, and "solutions" resulting from that mindset can often lead to worse results than more voluntary, less intrusive ones... sometimes including just ignoring the free riders.
If you want to ignore the problem, then you really need to get people to vote for ignoring free riders. We already do this - for example we allow charities to raise income tax free so they are free riders.
If you can't get people to vote to allow the group of free riders you want let off because you are opposed to compulsory taxation, then the idea just won't fly.