Consumer fingerprint based products and services are not uploading your fingerprints anywhere.

Fingerprint at border control is evil, but the ones on your phone or laptops are not the same.

Think of it this way:

When you type a password into a website, you are giving them (the website) the secret and they validate it.

When you use your fingerprint to authenticate to an online service/app, your computer checks your fingerprint and reports the result to the service. Your fingerprint (the secret) and all of the material you gave to set up fingerprint recognition (the identifier) all remain local and private.

Services need to trust your device for it to work because they are getting second hand information so they need to know and trust the middleman on your phone which is facilitated using cryptography developed to be used between them and your device manufacturer of course.