Only when that's on the banner the country is told to cheer under.
When it's a royal wedding, when it's "F D" or "FID DEF" printed on coins, when it's the requirements that all schools have collective worship of "wholly or mainly of a broadly Christian character"[0]… then suddenly it's a whole lot more like a theocratic monarchy.
From the surveys I've seen, the UK electorate seems broadly OK with the monarchy part of that (not that they have any real say in it because that's not how monarchy works), and regards the Christian[1] parts as harmless quaint tradition of no real significance.
[0] https://www.legislation.gov.uk/ukpga/1998/31/schedule/20?vie...
[1] I first wrote "religious", but large parts of the UK seem to still be scared of anyone with the "wrong" religion, though which one counts as "wrong" varies wildly.
The electoral system is the problem in both. The nuances are different, but by and large the causes are the same: alternating power between two parties where national issues and "the party" have become more important than "representing your constituency". A lot of the important issues fundamentally are national issues, so that's not really a surprise.