Men who have done a lot worse have been the head of the Anglican church...
Yes, we must not judge the Prince of Wales for his extra-marital affair when he was still married to Diana but those who truly follow Our Lord must pray for the healing power of the Almighty be upon those who are affected by this sort of sadness etc.
However, the Queen is not the head of the Anglican Church (or the Anglican Communion world wide) but she is the Supreme Governor of the Church of England. If my memory is correct, Henry VIII was the Supreme Head of the Church of England on earth but his daughter Elizabeth I sort of modified it to the Supreme Governor of the Church of England. Henry indeed was the head of it that he had every power to decide what sort of a prayer book should be employed for the liturgy of his church and insisted on the church to continue to use Latin when celebrating "mass" etc. It seems as though he only replaced the temporal as well as the spiritual authority of the Bishop of Rome (aka the Pope) over the affairs of the Church of Engalnd with his own. However, Elizabeth I sort of allowed the Church's independence from her own authority more and gradually the English monarch's role in the affairs of the Church of England became more nominal. Now we even have the General Synod though any matters such as the introduction of a new prayer book etc must be passed by the parlaiment still today.
The Anglican Church in New Zealand is called the Anglican Church in Aotearoa, New Zealand and Polynesia which is led by the Archbishop of New Zealand and the Queen of New Zealand is not the head of it nor the Supreme Governor of it nor the Defender of the Faith of it, I am sure. The Archbishop of Cabterbury presides the Anglican Commuion world wide but he is not, as in the case of the Bishop of Rome a.k.a. the Pope or the Holy Father in Rome, he does not hold the supreme jurisdiction over other churches that are in communion with the See of Canterbury because within the Anglican Communion each province is independent and autonomous (very similar to the Eastern Churches but not the same) over its jurisdiction matters.
Talking about the Prince of Wales, he has said that he would rather become the Defender of Faith as in all faiths than just of the faith of the Church of England which the Archbishop of Canterbury (the current one) rejected.
This idea of the prince obviously causes more disputes. If the English monarch is not the Defender of the Faith (the title of which was conffered to the English monach by the parlaiment) any longer, then, will s/he be the Supreme Governor of the Church of England ? If not and s/he can be a member of any church or a religious denomination or no religion at all etc etc, then, do we have to keep this family as the dynasty of the English monarch ? How about the Jacobite king - I think, if my memory is correct, somebody was telling me that the Duke of Bavaria or somebody would have been the King of England who is Roman Catholic - ?
Well, I only admire the office of king and it's a bonus in a way if the person who holds it is worthy to be respected etc but there are many people who are legally, constitutionally or historically aware of these matters around in this world that if the prince says this sort of thing, then, people start thinking and wondering or even questioning things.