Does a health care provider have a constitutional right not to participate in abortions?

Mark Rienzi has posted a fascinating new paper, The Constitutional Right to Refuse: Roe, Casey, and the Fourteenth Amendment Rights of Health Care Providers.  Here's (a portion of) the abstract:

The Court’s substantive due process analysis typically looks for rights that are “deeply rooted” in our history and traditions. Accordingly, this article addresses the historical basis for finding that providers do indeed have a Fourteenth Amendment right to refuse to perform abortions. This historical analysis shows that the right to refuse passes the Court’s stated test for Fourteenth Amendment protection. In fact, the right to refuse actually has better historical support, and better satisfies the Court’s stated tests, than the abortion right itself.

Beyond this historical case, a healthcare provider’s right to make this decision also fits squarely within the zone of individual decision-making protected by the Court’s opinions in Casey and Lawrence v. Texas, and protects providers from the types of psychological harm that the Court recognized in Roe and Casey. For these reasons, under Roe and Casey, a healthcare provider has a Fourteenth Amendment right to refuse to participate in abortions.

I have only had a chance to skim the article, and though it is well worth reading, I admit feeling some skepticism toward the constitutionalizing of professional conscience claims.  Whether or not providers were allowed to refuse to participate in abortion over the course of our nation's history, I still think the constitutional question has to take a back seat to questions about the definition of the professional role.  If a state hospital posted a job description for an "abortion provider," I have a hard time imagining the doctor hired for that job successfully challenging the state's decision to fire him for refusing to provide abortions.  Let's say that the state wants, via its professional licensing authority, to establish a category of abortion providers as a subset of the broader category of obstetricians.  Would it be constitutionally permissible for the state to require a willingness to provide abortions as a condition of licensing for that category?  It's difficult for me to see where the constitutional violation kicks in -- perhaps when the state sweeps too broadly with the requirement, forcing all obstetricians to provide abortions as a condition of licensing, for example?  In any event, I need to spend more time with this article, and you should too.