There are well-established rules of decorum when meeting a member of royalty, a President etc. Some of these rules go back centuries. They add a certain level of civility to what seems to be becoming an ever-coarsening world.
There are certain standards that civilized people follow. It's sad to see so many conservatives rejecting those standards. Such rejection for rejection's sake is more akin to the values of the French Revolution.
There is no royalty recognized in these United States. There are citizens who are all equal and foreigners who, while they should be treated with respect as all mankind should, are somewhat less than citizens
Some of these rules go back centuries
"Because we've always done it that way" is not a good reason for doing anything. The rules for treating royalty differently come from the day when royalty had the power to do you harm or good. Since royalty had that power it was important to suck up to them. Those days are long past (unless you are on their turf)