Will my customers' payment methods be saved?
If you utilize scheduled payments with auto-bill turned on, then your customers' card information will be saved for future payments after initial entry, saving them from needing to re-enter the information each time. To turn this off, then simply uncheck the auto-billing option when configuring scheduled payments. Learn more here.

Another way that card information might be saved is through Link, if this is something you utilize. This is one of the options under Stripe Elements, and this can be controlled by opting in/out of Link through Stripe.
Note that individual invoices (with no scheduled payments) should not save customers' card information.