The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.I'm assuming that this means that the citizens of each state are entitled to all federal privileges and immunities, not each other states' privileges and immunities, since this the Constitution of delegated federal powers. Each state has its own constitution that governs the people of the respective state.
-PJ
Citizens of one state have the privileges and immunities of another state when they are in that other state. Not in their own state, where the state defined privileges and immunities differ. Otherwise, the most or least restrictive state laws would be in force everywhere.
Any law saying it is illegal to cross state lines for an abortion (where it is legal) is prima facie unconstitutional.