Allpoint / Moneypass ATM at Madrid–Barajas Airport?

I doubt it, since those networks are mostly US based, with some limited countries included. Your ATM card should still work, just not fee-free. In Spain, most ATMs will charge a fee for use (3 to 7 euro) and nearly all will offer DCC, so be aware of that.

While no guarantee, I did use a Unicaja ATM with no fees and in the past Rural Caja ATMs without a fee. But it does vary, both fee or no fee and the amount of the fee.