Denti
Our SOP recommends (but of course you can deviate) that both use MAP if you have two FMC and two GPS receivers. That still leaves you with the raw data ILS indication on the PFD which is an approved crosscheck.
Isn't that putting the cart before the horse? The ILS display isn't there to crosscheck the map, it's there to be flown and for PF to act on the deviations indicated. Flying the map is really the realm of GNSS approaches is it not? We can still fly an ILS with an ANP > 0.3 after all.