I didn't ask the postal clerk about a debit card. I tried to use Amex, she said that would not work, and I had the cash ready to go. I suppose if they accept that to buy stamps with cashback, you could effectively get your money order that way (at least for a small amount such as this).

I got the sense that the reason you couldn't use cash or credit was because this was a county office. Sort of akin to using a contract DMV location if those exist in your particular state. I have no complaints at all about it - it was totally low-stress, no queue (just one other guy with an appointment near our time), and a very friendly clerk helping us out.

The only thing they could possibly improve about their process is to insert a short blurb in the appointment email to bring exact payment in one of the accepted forms. The county's portion of the processing fee was paid with a credit card: only the portion sent to the federal government was the MO.