Yes! However, Health Savings Account cards and Flexible Spending Account 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. You'll need to reach out to Stripe to get this set up. If your business needs to accept these cards, you can reach out to Stripe by clicking here.
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. You can learn more about declines here.