Thank you for correcting me (rolling eyes) now go correct Wikipedia:
Now go read the bit of Wikipedia about the Parliament Acts which allow the Commons to pass legislation without the approval of the House of Lords (...you might also want to ask yourself how the heck and act like that ever got passed in a "theocratic monarchy").
You go on to say "the Queen must otherwise keep the fuck out of politics or else."
Right: "or else". She has real powers which, if she exercised them, might lead her to lose those powers.
No, she has theoretical powers that if she even tried to exercise would trigger the "or else". Even making an allegedly political comment causes a shitstorm.
if you have a monarch, you aren't a democracy;
Since you seem to regard Wikipedia as the fount of all knowledge: Constitutional monarchy is a form of democratic government in which a monarch acts as a non-party political head of state within the boundaries of a constitution, whether written or unwritten. (The article goes on to describe the UK as a Constitutional Monarchy).
if you have an official state church, you aren't secular.
...true, but if the state church is subordinate to an elected parliament, you don't have a theocracy, either. Your favourite source, again: Theocracy is distinguished from other, secular forms of government that have a state religion, or are influenced by theological or moral concepts, and monarchies held "By the Grace of God". In the most common usage of the term, some civil rulers are leaders of the dominant religion (e.g., the Byzantine emperor as patron and defender of the official Church); the government proclaims it rules on behalf of God* or a higher power, as specified by the local religion, and divine approval of government institutions and laws.