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.