The ones who were doing that "thinking at the time".
Both of them?
I'm saying that those who thought the 14th applied the BOR to the states thought the P&I Clause would be the vehicle for doing so. Those who thought that way were a) in the distinct minority (a handful) and b) wrong.
The overwhelming majority of those who passed the 14th did not think it applied the BOR to the states in any way, shape, manner, or form. This was confirmed by legislation they attempted to pass subsequent to the 14th (legislation that would have been unnecessary if the BOR applied to the states), the U.S. Supreme Court ruling in the Slaughterhouse Cases a mere five years after ratification (which the Congress then did nothing about), and subsequent court rulings for the next 60 years.
It was only then that activist courts starting using the Due Process Clause of the 14th (NOT the P&I Clause) to selectively incorporate the BOR. Parts of the BOR are STILL not incorporated.