Possibly, but the above insult seems to have zilch linguistic awareness and the rebuttal is unconvincing. The Cambridge dictionary
defines "theocracy" as "a country that is ruled by religious leaders" and the King is both head of state and the head of the Church of England, so a religious leader, so it seems pretty clear that Britain is still a theocracy, as well as now basically a democracy. Edit to add: there are still bishops sitting as "Lords Spiritual" in the House of Lords, too. I thought they lost their seats along with most hereditaries but apparently not.
That's not to say it matters much, or is a problem, in current practice. But how did you decide it obviously isn't?