In Freedom's Law, Dworkin draws the distinction between constitutional persons and actual persons. He argues that the constitutional status of fetuses, slaves, and corporations doesn't actually depend on biology but on the legal definition of personhood. Fair enough.
But the question also presumes the constitution has ANYTHING at all to say on these issues. On some it does, but I am at a loss to find the concept of a fetus written anywhere in the constitution. I'm sorry people, the constitution just doesn't say aye or nay on this issue. Anyone who claims they can find it is engaging in pure sophistry.
Interestingly, if biologists and philosophers managed to come to a consensus on what a person is then it would be still a question whether constitutional jurisprudence would need to alter its definition. That depends whether one holds an originalist interpretation (what did the authors of the constitution mean when they referred to persons) or a best available theory interpretation which would update our idea of personhood or due process of law depending on the best available current informaton about what that requires.