States aren't allowed to be sanctuary for criminals from other states. I'm not clear on whether active pursuit is required, but if the governor of Texas produces a legal warrant for a person to the governor of California, they are required to act on it. They may not have to perform a manhunt, butbifnthe person is stopped for speeding or something, they would likely be required to arrest them. The only exception is that a state can keep a person for criminal prosecution and imprisonment first, which isn't relevant for an out of state abortion.

The state could argue that a warrant for performing an abortion isn't legal as the requesting state had no jurisdiction where the supposed crime occurred. This isn't required by the law though, so it may be up to the arrested person's counsel to raise that argument, keeping all the risk on the person still.

https://constitution.congress.gov/browse/essay/artIV-S2-C2-1/ALDE_00013632/#:~:text=A%20Person%20charged%20in%20any,having%20Jurisdiction%20of%20the%20Crime.

It's interstate extradition. Unless California is going to ignore the executive branch, it's entirely unenforceable.

Sure.

https://www.law.cornell.edu/constitution-conan/article-4/section-2/clause-2/overview-of-the-extradition-interstate-rendition-clause

Article IV, Section 2, Clause 2:

A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.

Now arguably one can say that a California person did not flee but that argument has not been explored from what I can gather. Generally rendition seems to be granted given an indictment in another state.

In 18 U.S.C. § 3182 (which enables interstate extradition): Whenever the executive authority of any State or Territory demands any person as a fugitive from justice, of the executive authority of any State, District, or Territory to which such person has fled, and produces a copy of an indictment found or an affidavit made before a magistrate of any State or Territory, charging the person demanded with having committed treason, felony, or other crime, certified as authentic by the governor or chief magistrate of the State or Territory from whence the person so charged has fled, the executive authority of the State, District, or Territory to which such person has fled shall cause him to be arrested and secured, and notify the executive authority making such demand, or the agent of such authority appointed to receive the fugitive, and shall cause the fugitive to be delivered to such agent when he shall appear. …

Overall it seems to me that a person charged in another state will be extradited as one could interpret residing in California as “fleeing” say Texas’s jurisdiction.

Edit: see my edit on my top level comment. I’ve dug into this issue in a bit more depth and it feels like this is less of a clear cut issue than I initially thought. Thank you everyone for pointing out the flaws in my logic.