Can I apply for a visa to Thailand while on probation in the USA?

First of all without a doubt I would not even attempt to apply until at least one month after you are off probation. Secondly if you have a felony for anything having to do with trafficking of drugs and narcotics, murder or attempted murder, or pedophilia, I suggest you don't even bother applying at all save yourself the expense, stress and waste of time.

There is no background check

Dude it’s fine

30% American has criminal record yet they are out of country so don't sweat it.

Ofcourse, you can apply from the jail too

You can definitely apply but whether you pass or not is another story. Though you said you still have a few months of probation, so no point in even applying as processing time is usually around a month. At earliest you’d want to apply a month before probation ends, but it might not be a bad idea to see it through to the end, especially if your record will be expunged after probation, just in case. To be fair, I didn’t have any background check I think when applying, but who knows if they’re conducting any checks themselves. Maybe not, or maybe yes. What’s safest is seeing it through to expungement if possible, or at least post parole, then applying. Of course, YMMV and you can apply more than once anyways.

Also, you could consider applying in Vietnam or something like that if you’re very eager to get to Southeast Asia after your parole is over. Not Thailand, but at least you’d be in the region.

Most expats have criminal records here, I wouldn’t worry

Unless a specific embassy or consulate requires it there are no general background or criminal record checks. There have been a few posts with European Thai Embassies asking.

You need a clean record so no is the answer. I'd also suspect that your probation wouldn't allow you to be living on another country.

Probation for ?