Mostly, websites don't store any card information on their own server on payments (deposits or withdrawal), only the accredited third party payment processors store it and see it and you need to trust them too as part of their privacy policy or tos, idk which one or both.

Yes, accepting wide range of payments is a good move as it broadens the service's views and kind of users to entertain, there are lots of "crypto casino" accepts visa/mastercard deposits and direct to bank withdrawals too.