While the way this claim is written can be a little harsh when it comes to the weight of what this claim includes, such as religious beliefs, it has been said directly that Kamala Harris supports the Women's Health Protection Act and she is even a co-sponser for it, which can be found directly on the bills co-sponsers list on congress.gov. While this is not necessarily a negative in many eyes as womens rights are extremely important, supporting this act includes getting rid of protections from the Religious Freedom Restoration Act of 1993, which "prohibits the government from “'substantially burdening a person’s exercise of religion.' ” The WHPA states that "this Act supersedes and applies to the law of the Federal Government and each State government, and the implementation of such law, whether statutory, common law, or otherwise, and whether adopted before or after the date of enactment of this Act, and neither the Federal Government nor any State government shall administer, implement, or enforce any law, rule, regulation, standard, or other provision having the force and effect of law that conflicts with any provision of this Act, notwithstanding any other provision of Federal law, including the Religious Freedom Restoration Act of 1993". In more simple words; the Women's Health Protection Act (WHPA) takes priority over all federal and state laws, whether they were created before or after this Act was passed. This means that no government can enforce any law or rule that goes against what the WHPA says, even if other federal laws, like the Religious Freedom Restoration Act of 1993 (RFRA), are involved. WHPA also includes provisions that allow individuals to bring legal action if they believe their rights under the Act have been violated. To sum things up, yes, since Kamala Harris supports the WHPA, she is also supporting anyone who denies facilitation an abortion due to their religion, to be sued.
https://www.congress.gov/bill/117th-congress/house-bill/3755/text
https://www.breitbart.com/politics/2024/10/02/fact-check-jd-vances-debate-claims-on-botched-abortions-catholic-nuns-are-correct/