Hey Angry, have you heard of of false dilemmas?

Imagine a cup of coffee to which I add a droplet of orange juice. Is it still a cup of coffee?

A rational person might either say "yes" or "yes with a drop of orange in it". You, on the other hand, would insist it is "in short: not coffee" because you reserve the term "coffee" for only the purest cups of coffee.

Officially, the UK is a ceremonial monarchy. The monarch does not make law (unlike executive monarchies such as Bahrain or Jordan), they merely rubberstamp their parliament's decisions. (There's a reason for that.

The parliament is bicameral. The lower house is elected representatives. It is secular, there are no religious conditions required to vote. (however, it is not republican; MPs must swear allegiance to the monarch).

The upper house is a mix of appointments and hereditary peerage. While yes, 26 of ~779 members are from the state church, the remaining appointees/peers are not required to adhere to a religion.

Legislation must pass both houses - both elected and not; the unelected house has several limits binding it, which prevents it from indefinitely stalling legislation.

Ultimately, the lion's share of power in the UK belongs to the Government (that is the elected MPs of the largest political party in the house of Commons). Most of the parliamentary timetable is reserved for their agenda. If their party is united, they can outvote all the other MPs. The house of Lords can refine but ultimately can't reject their legislation. The monarch will rubberstamp it. Religion's official voice is limited to 26 out of ~1429 members, which is 1%. This is a droplet of juice in an entire pot of coffee. To argue otherwise is fatuous.