I don't work for SubscribeStar so I cannot speak for them on what they will or will not accept.
But to answer your question in a generally sense, that really depends on where you are. Everything I said before and below are 100% true in my country, and they are mostly the same in most countries but not always the same. So caveat emptor.
Where I am, merchants have the choice of accepting both debit & credit cards, or credit cards only, or debit cards only, or none at all. It's very rare that a merchant will accept credit cards but not debit cards, as it generally cost them less to accept debit cards. It's much more likely that a merchant will only accept debit cards but not credit cards for that very same reason.
Also, it's uncommon in the western world, but sometimes merchants will deny acceptance of cards based on the card issuer's geographics location. (e.g. It's not uncommon for mom & pop shops in non-tourist areas of Japan to not accept cards not issued by Japanese banks.)
And in some places, in rare cases, even specific credit cards from their own countries might be denied because not all credit cards with the same processing network logo cost the merchant the same percentage of the transaction as a fee. Where I am, some fancy upscale cards sometimes also takes a larger percentage of the transaction from the merchant as the processing fee, and a few merchants have simply said no to them. But this is mostly limited to in-person transactions.
One last thing, and this is a very common misconception. Visa or Mastercard are payment processing networks, not card issuers. Your credit cards are issued by your banks. AmEx may be a little different but then again, most AmEx cards are technically charge cards, not credit cards. Bottom line is, AmEx is a little weird, ok?
