I usually stay onsite at least once every year (sometimes twice), for a few nights at a time. My last few stays have been at the PPH (before that I stayed at the GCH), and I booked with a debit card each time. Most debit cards these days - as long as they have Visa or Master Card logos on them - can be used anywhere or in any way a credit card would be used. There may be a few exceptions, but most can be used that way.
I've handled my reservations several different ways. I have paid the entire amount due on the debit card in advance so that it was all taken care of before arrival.
I've also paid some of the amount due in advance and paid the rest upon check-in - and I've paid the balance due at check-in with both cash
and with a debit card. The CM stopped any other charge from appearing on my card except for the incidentals hold (which was lifted about 5 days later).
I've also paid some of what's due in advance (a deposit is required for the Disney hotels unless you have a special offer of some kind that waives it, or unless you pay the entire amount due up front), and then paid the remainder of the room off in multiple
Disney gift cards...except for that the CM at the front desk did not apply the gift card credit to my total due when I checked in and they went ahead and applied the full balance due to my debit card anyway. They also put the balance on a debit card that I didn't tell them they could use (they just pulled a card number that was in their system).

The CM claimed that gift card credits are usually deducted
at the end of one's stay, and that the total bill is adjusted at that point. I've been told by a different CM, however, that they have a way of stopping those automatic charges to your card at check-in and can apply the gift card credit at check-in instead of at check-out.
Last year I was not required to pay any kind of deposit up front for my PPH stay because it was a special offer. I even asked them if I could pay something up front and they wouldn't do it that way (it was a reservation made through a different department of Disney and not through the regular channels). This was all well and good
except for that they still tried to charge me for my one totally free night anyway. Fortunately I caught it before I checked out and got them to stop the charge before it appeared on my debit card.