I don't feel comfortable giving Aristois my credit card
We use Stripe. We do not see your card information. Stripe is as safe (probably safer though) than PayPal is.
Well, there isn't a button for Apple or Google Pay
You will see the buttons on devices that support Apple Pay and Google Pay, and that have been set up for such payments already. (For example, an iPhone or a user who has added a payment card to Google Pay
I also tried to use my MasterCard gift card but it said that it didn't accept that type of card.
Your gift card has declined the transaction, not Stripe. There's not much we can do about this as it's not on our end. If you're using a debit card that requires a PIN code, you cannot use it. You also must ensure the gift card is registered to use online via the provider.