As a HS coach and runner I love when community runners use our school’s track (at appropriate times) - though I don’t think my admin feels the same way.
That said, the notion that all public school athletic facilities are paid for by tax dollars is not true. My school’s track was 100% paid for by booster club funding, largely donations and hosting track meets. The same is true for most of our athletic venues.
And many resources at public school are paid for by tax dollars and are not freely available to everyone. Our science labs are not open to the public in the evening, community members don’t have access to our school library. The copiers, printers, ink, and paper aren’t available to all. Tax dollars also pay for military weaponry and NASA equipment that are unavailable for general use by taxpayers. Don’t use a lazy argument to justify what you want.
Many tracks are open to the public, many tracks are locked but will not care unless you cause a problem, a few tracks are tightly closed and expected to be used only by students. Use good judgment.
In almost all cases the likelihood of being arrested is very low unless the track user is nasty or the school personnel/police officer is nasty or feels a threat.