I arrived at the airport on 6 Jan 2020 and got on the Havaist IST-5 bus with my credit card. There‘s a contactless card reader on the bus. There are also some vending machines at the bus parking spot, so in case your bus doesn’t support credit cards, you can easily buy an Istanbulcard nearby. If you don’t want to buy the card, you can also have the havaist app installed on your phone in advance, so that if they don’t accept card payment you can then load it with money and pay. By the way if you decide to travel in Istanbul with public transportation, getting an Istanbulcard is really convenient and you can also get discounts on transportation fees. Hope this helps and enjoy Istanbul :) Cheers, Kol!
Update: I spot a havaist bus today and they have a visa/MasterCard logo on the door so I believe you’ll be fine [visa/master logo on the bus] (https://i.sstatic.net/MSi7X.jpg)!