More details on accepting HSA/FSA cards can be found on the Stripe website:
HSA and FSA cards require that your business have a special classification (called an MCC) set so that the card companies know that your products and services are directly related to a patient’s medical needs.
If your business needs to accept HSA or FSA cards, please get in touch so we can make sure that your account is properly configured to accept these card types.
And bear in mind, just because an account is enabled to accept HSA or FSA payments, doesn’t guarantee a card won’t still be declined. Card issuers are still at liberty to authorize or decline any payment as they would with any other type of credit card.
https://support.stripe.com/questions/can-i-process-hsa-fsa-cards-using-stripe