To make it even more complicated, regulators often hold contradictory views. They want to see increased safety, but in the same breath will announce actions against companies for violating privacy. This is a super-difficult balance to strike.
Specifically for Stripe, I trust them. So if I see that a new start-up is using them rather than rolling their own solution, that increases my trust. But it means there is now a big giant server in the cloud with millions (billions?) of identity documents that is worth a lot of money for hackers.