Alright controversial opinion.
Yes you can (and should) argue that Trump was rude, unprofessional, and just being a general dickwad while meeting with Queen Elizabeth.
But any complaints that he "didn't follow Royal Protocol" can get take a flying **** at a rolling donut. The Queen of England doesn't get to set special rules (or have others set rules on her behalf) for how other heads of state have to act around her.
Trump should have treated her with a lot more basic respect and... just basic human interaction standards then he did but, and it pains me to say anything apologetic about Trump, him not following some subservient routine in body language and Royal Court procedures doesn't bother me in the least.
Trump is not a citizen of the British Empire. He is no more obligated to bow to the Queen then the Queen is to salute Trump for being Commander in Chief of the American Armed Forces.
TL:dr - I'm as mad as everyone at him not treating her with the respect due another head of state, but that's it. He had every right to act around, talk to, interact with, and maintain the same poise and body language with Queen Elizabeth as he does with every other foreign head of state.
And it bugs me when they do this in regards to the Pope as well.