I think a bit of differentiation could be good, but I draw a distinction here. You get to choose among choices available to you. So unless "not paying for the military" was an option written into law by congress, you could not select that option. And it would be unlikely to be offered, for many reasons, not the least of which is that everyone benefits from the military just by virtue of living within the borders of the US.
I don't think it should be a menu where each citizen gets to select from a huge range of options. I think for some things that would work, but there are many things too fundamental to let people opt in and out.
More people who are able to be productive members of the workforce, better mental health from improved financial security, and less cost from preventative rather than responsive treatment.
That also gets to the heart of the problem - not everyone recognizes the benefits that I've suggested from a more universal healthcare system.
I would also contend, that I don't see the benefits from the level of military spending that we have.
The healthcare system is interwoven with rules and regulations. For instance, we already have tax rules depending on your yearly FSA/HSA contributions, tax deductions based on how much money is spent, and most importantly the Obamacare rule that one must have insurance or suffer penalties. Would another exception break the system?
Having individual discretion over what tax dollars goes to leads to an unmanageable mess for those trying to actually create a budget. Additionally, sometimes a national priority and the hard choices that goes with that means having taxes spent on things that aren't necessarily popular with the entirety of the electorate.
The control over the budget comes (in theory) with voting on a house member who aligns with your goals for the budget. Yes - in theory.