There are clearly serious concerns about the UK heading into an authoritarian state. The right to protest has been so seriously curtailed that even innocent people who aren't protesting can end up arrested and detained for hours.
Gotta hand it to the US and their Constitution, it definitely does a better (though maybe not perfect) job protecting citizens from government over-reach.
The US appears to have much stronger constitutionality granted freedoms than most other countries.
A well functioning liberal democracy needs a means of kicking out the government, and strong limits on the kind of laws a government can impose, through constitutional protections.
Personally I don't think that "decrees" or executive orders or whatever are a problem, as long as they are within the constitution and the population can vote to kick out whoever made them. Much worse is when the constitution, or personal freedoms that should be enshrined, are violated "democratically" with a majority support.
The last proclamation/coronation was a long time ago so most people have no experience but I suspect nothing has changed. These are 'sacred' occasions and public dissent will not be allowed during official events.
Gotta hand it to the US and their Constitution, it definitely does a better (though maybe not perfect) job protecting citizens from government over-reach.