The Queen's kids bow and curtsy to her in The Crown, which seems like a waste of time better spent hanging out with corgis, but hey, that's just me, as in, a person who doesn't know how to curtsy. I think you get in one of the ballet positions, then go weak at the knees for a few seconds? It's unclear.
The Answer: It seems like the answer is yes, but it's complicated. First of all, the official Royal Family website, royal.uk, notes that there are "no obligatory codes of behavior" you must observe when meeting a royal, but that the "traditional forms" of a bow from the neck (for men) and a curtsy (for women) remain common. Regrettably, there's no mention of the acceptability of a high-five or finger guns.
The official website doesn't mention the rules around the royals greeting each other, either. A historian named Marlene Eilers Koenig told Hello! in 2018 that those with the title "royal highness" only curtsy or bow "to the sovereign," aka the King or Queen, and not to the other members of the family with their same title and status. According to Koenig, the royal kids are expected to start bowing and curtsying around the age of 5.
And according to the New York Times, which published a detailed guide to curtsying in 2018, Princess Catherine is required to curtsy to "royal princesses by blood," since she is a royal princess by marriage. However, if her husband Prince William is with her, those blood princesses (super metal band name, by the way) have to curtsy to her.
That's not too much to remember, right?