The difference here is that Jackson, Mississippi is not in the same metro area.
The Supreme Court said specifically that a state can not offload its constitutional responsibilities onto another state.
But is it actually doing so? You'd have to show that if there were no clinic just across the border in Las Cruces (which was already getting significant business from Texas) then El Paso wouldn't have one that did meet the Texan standards to argue that it is offloading its responsibilities. Equating the situation in El Paso with Jackson's is ridiculous. Since the El Paso metro is larger than McAllen, which is going to continue having a clinic, I fail to see how any reasonable person would conclude that El Paso is going to be deprived local access to abortion services.
Wouldn't it deny access to El Paso patients without a passport?
No. Las Cruces is in New Mexico, not Mexico.