To their credit, Stripe have previously given public and pretty unambiguous assurances that if you do decide to move away, they will co-operate to transfer the sensitive card data in their vault to another service, subject to some reasonable concerns about PCI compliance and the like. So at least from Stripe's side, that should mean you don't have to trouble your customers about re-entering details.

I don't personally know anyone who's actually done this, so I can't comment on how well it works in practice.