The equal protections clause of 14th amendment prohibits unequal application of the law. The business next door can do anything they please with their building

The equal protections clause of 14th amendment prohibits unequal application of the law. The business next door can do anything they please with their building lawfully, but the protected landmark building is prohibited by law from doing the same things. There's literally a set of separate set of much more restrictive laws the owner of a protected landmark has to follow that a business not similarly affected does not. Obviously much less is at stake here than having a separate set of laws for whites vs blacks, but it's the same principal.