Actually, it is a constitutional issue. Under the British constitution, one of the monarch's titles is Fidei Defensor, defender of the faith. Moreover, even though bishops of the C of E sit in the House of Lords, Queen Elizabeth is the head of the Church, superior to the Archbishop of Canterbury. If she were to assent to this bill, it would fly in the face of 2000 years of Christian doctrine. So the question is, will she uphold her royal oath to God or not?
No, it is not. It has nothing to do with any element of the British constitution.
Under the British constitution, one of the monarch's titles is Fidei Defensor, defender of the faith.
While Defender of the Faith is one of the Monarch's titles, the titles of the Monarch are not part of the constitution. They are considered a 'style' which can be changed at will by Parliament (Her Majesty's current style is set by the Royal Titles Act 1953, and renders the style only in English, so Fidei Defensor is not strictly part of it, but a translation). It's not part of the constitutional law.
Moreover, even though bishops of the C of E sit in the House of Lords, Queen Elizabeth is the head of the Church, superior to the Archbishop of Canterbury.
She is Supreme Governor of the Church of England, certainly, but she is not Head of the Church of England - in fact the term Supreme Governor was deliberately chosen in order to avoid the use of the term Supreme Head (Henry VIII and Edward VI had used the term Supreme Head, and it had caused considerable issues, so Elizabeth I had it changed to Supreme Governor).
The Thirty-Nine Articles of the Church of England of 1563 set out precisely what the Monarch's powers were and were not in terms of their powers over the Church. The 37th Article makes it clear that all powers of the Monarch in regards to running of the Church, and to its influence over government are delegated to the Ecclesiastical or Temporal authorities - Parliament in other words.
If she were to assent to this bill, it would fly in the face of 2000 years of Christian doctrine. So the question is, will she uphold her royal oath to God or not?
Yes, she will. Which is why she cannot intervene - because of this section of the Coronation Oath that she swore: And will you preserve unto the Bishops and Clergy of England, and to the Churches there committed to their charge, all such rights and privileges, as by law do or shall appertain to them or any of them.
By law, and by the Articles, the right to make decisions on laws that go through Parliament is a privilege of the Bishops of England - the Lords Spiritual. She swore to preserve that right - not to overrule it.
That is the Oath she swore.
The Queen is not a tyrant. She does not get to overrule Parliament, except on a very precise set of issues.