If your bank supports Oauth it won't share your credentials:

>Stripe generally defaults the authentication flow to OAuth if available at the financial institution....OAuth is an open standard authorization protocol that allows users to let applications (for example, Stripe) access their information within other applications (for example, bank apps) without having to share their login credentials.

But for banks without Oauth you DO give your credentials to Stripe:

> For these banks, end users provide credentials to Stripe or one of our trusted partners.