Question: with Constitutional carry one does not need a permit. How does this effect reciprocity with other states that require permits?
Many states that have Constitutional carry also provide CCW permits, primarily for their residents when they go out of state to those states with reciprocity deals. There are even a number of states that allow non-residents to get a CCW (Utah and Florida come to mind) that allow you to concealed carry in about 35 states that have reciprocity deals with them, even if you live in 2A hell-hole like California.
It does not affect permit status. All states which have restored Constitutional Carry have retained their shall issue permit systems for the advantages which permits offer.
The Texas proposal would keep their current permit system in place.