I agree, as the head of the State and the highest rank in church, the souvereigns and heirs are somewhat expected to show some interest.
Imagine QEII publically announcing that it is some kind of "opium of the people" and she can't really be bothered.
They all (apart from some of the younger generation) seem to succeed in walking a fine line: don't be too religious or worse believe in spirits and alternative religions: shades of Wilhelmina and Juliana of the Netherlands and Alix of Russia and in the younger generation the norwegian princesses with Maertha conversing with angels and MM being a tad too interested in psalms and music.... but on the other hand don't be too indifferent as not to put off people with faith :I think that Freds inability to stay thru a complete service (and we are not talking about those extremely long orthodox rites) angers a lot of religious people.
QEII is a great example: she attends ceremonies and services on sundays spend at Balmoral or Sandringham, as is/was custom in her generation and she occasionally mentions the heavenly help and the relief and support her faith gives her, but she does not overdo it. How much church she really attends to is left to your own guess, as she is said to pray in her own chapel in Buckplace and Windsor (now we can believe that or not...)
Religion is not so very much mentioned in everyday life here in Europe, quite opposed to the States, where the heavens are called out at every turn. (Maybe this is changing here in Germany as well, as I was quite surprised to hear the chancellor say, that her prayers were with the families of the victims of the school shooting, it used to be "our thoughts" not "our Prayers")