The correct reference is to the Due Process Clauses (see 5th and 14th Amendments). Both refer to not being denied “life, liberty, or property, without due process of law”.
Perhaps the most problematic issue is “no person” shall be denied instead of “no citizen” shall be denied.....
One would logically determine that a United States Bill of Rights would apply to Unites States citizens, and not, say, citizens of Costa Rica, Cuba, Zimbabwe, etc.
That is the argument I heard recently from a pro-choicer. That under the 14th Amendment (all persons born etc.) the fetus is not a citizen and therefore has no constitutional rights. The mother is a citizen and therefore has the right to determine what medical procedures are best for her. I haven’t really come up with a good rebuttal to that one yet.
This is why I would like to see a constitutional amendment stating that life begins at conception. As far as I know there has been no attempt at this.