In the comments, the question was reframed as:

What strikes me as potentially hypocritical is on the one hand the Monarchy is saying (by agreeing to Bill of Rights Act) that they accept that they are not installed by the will of God (to placate an uprising), but then contradict this with every piece of stationery they issue. The Bill of Rights Act is an immensely important document for British constitutional law and the Monarchy (whom it sought to put under the rule of law) have a motto which directly contradicts it

At the core, you are confusing political culture with political institutions. Political institutions are things like laws (including constitutions), courts, legislatures, offices - all the formal bits of how government works. Political culture is a largely intangible set of symbols and acts that are used to represent values.

The two interact in some ways. Institutions make use of symbols to communicate. Sometimes institutions formalize symbols (for example, by adopting the design of a crest or flag).

However, the two are ultimately incommensurate. There is no legal value to a motto; regardless what the motto says it does not really tell you anything authoritative about how the government functions. What it does do is provide a symbol which tells you something about the culture that produced it. I'm no expert in English political culture, but this looks like a fairly normal case of preserving an antiquated symbol to keep a tie to the past.

There are plenty of similar issues in all (or most) cultures. Societies are multi-faceted and you shouldn't expect all the pieces to line up in an orderly, rational way.

There is a lack of references here, which I acknowledge. In keeping with the Good Subjective/Bad Subjective principle, I am basing this on my background as a political scientist.

At the core, you are conflating political culture with political institutions. Political institutions are things like laws (including constitutions), courts, legislatures, offices - all the formal bits of how government works. Political culture is a largely intangible set of symbols and acts that are used to represent values.

The two interact in some ways. Institutions make use of symbols to communicate. Sometimes institutions formalize symbols (for example, by adopting the design of a crest or flag).

However, the two are ultimately incommensurate. There is no legal value to a motto; regardless what the motto says it does not really tell you anything authoritative about how the government functions. What it does do is provide a symbol which tells you something about the culture that produced it. I'm no expert in English political culture, but this looks like a fairly normal case of preserving an antiquated symbol to keep a tie to the past.

There are plenty of similar issues in all (or most) cultures. Societies are multi-faceted and you shouldn't expect all the pieces to line up in an orderly, rational way.

There is a lack of references here, which I acknowledge. In keeping with the Good Subjective/Bad Subjective principle, I am basing this on my background as a political scientist.