There's technically some ability for parents to opt-out of the delivery of the blood spot to the state, by written request before/during the delivery process.

But that's so discouraged, and the normal process is so automatic and hectic, that it's very rare. Few even realize the blood-spot permanent-collection is happening.

There was a proposed bill in 2015 to require signed consent before the collection, but it was defeated. See very end of:

https://nakedsecurity.sophos.com/2015/11/12/california-colle...

Don't live in California or those other states.

Much as you can opt out of the Second Amendment protection of firearm ownership by moving out of the US.