If you were on active duty you can liberally choose your domicile, as in, where you either were from or intend to retire to, current station, etc. Do that to your advantage, naturally.
For example if you "lived in" New Hampshire with no tax, bought a car in state (for simplicity), registered it there for six months, then moved ("moved") to a state with sales tax, they usually won't get you.
The problem with sales/ use tax is either a sale or a use can get you. Regsitering a car bought anywhere in a use tax state is gonna get you, unless (usually) you can prove you've "always had it" when you moved there.