Do hostels in Iraq accept cards or only cash?

I would not rely on card payments at all. Hostels are not equipped to take cards. The best plan is to have a good amount of local currency, the Iraqi dinar, and US dollars on hand for your hostel payments and other daily expenses.

You'll need cash for sure. My experience in Iraq was that paying with a card at hostels is not an option. The owners are wary of transaction fees and prefer the simplicity of cash. I’d advise you to bring a good amount of clean US dollars to exchange at a bank or a money changer. You can also withdraw some Iraqi dinars from a bank, but cards are not a reliable way to pay for a stay.

Don't even bother with cards. I was just in Baghdad last month and did not see a single hostel that accepted a credit card. It's a very cash-based economy. I stayed at a small guesthouse near the city center and the owner was very clear that they only accepted cash. You should assume that all your hotel payments will be in cash, preferably in clean US dollars.

You'll be using cash for almost everything, especially for hostels. While some of the major international hotels in Baghdad or Erbil might take cards, you will not find a hostel that does. The local currency is the Iraqi dinar, but for larger payments, like hotel, it's often preferred to pay in US dollars. The financial system is still developing, and you can't rely on being able to use a card for anything other than at a few major international merchants.