Reality: These things are actually more based in culture and tradition than law.
Spot on on the being based more on culture and tradition than law though.
Trump is not equivalent to the Queen in role. The Queen is supposed to be a figured head only, a bit like the American flag. That's why this news is controversial because it's an abuse of position.
Real power in the UK rests solely in the House of Commons.
The last monarch that forgot that publicly had their head cut off in 1649.
That fact is celebrated every opening of Parliament when they slam the door in the face of the Queen's representative Black Rod, exactly so that she remembers.
You might not like the unwritten rules that govern the UK but they've worked pretty well so far and have been malleable enough to be reformed whenever there's been a problem.
I (name) do solemnly, sincerely and truly declare and affirm that on becoming a British Citizen, I will be faithful and bear true allegiance to her Majesty Queen Elizabeth the Second, her Heirs and Successors, according to law
After which the citizen is issued a passport by Her Majesty’s Passport Office.
If we compare and contrast with America, nobody needed to swear allegiance to Trump at the border. They let in a bunch of people who would have actively and publicly wanted him gone. One of these two countries is pretending that birth literally should confer special privileges.
[0] https://www.gov.uk/government/publications/british-citizensh...