Les, there's a whole other discussion to be had about Ron Hutton and "Stations of the Sun", which I've read - I've also met and discussed several aspects of this thread with Ron himself. He's an academic historian, not a folklorist and will only record stuff which has some form of written evidence to support it - he also puts his own interpretation on the "facts" which may or may not be trustworthy. I'm not sure how his book supports your more sweeping statement.
Guy Fawkes wasn't burnt for his Catholicism but because he was a 17th century terrorist, a mercenary who was part of the plot to blow up the king and government of the time.   Yes, there were burnings of people deemed to be heretics under both Catholic and Protestant rulers, but don't forget that in England witches were put to death and in Scotland they were burnt. Not just a question of the variety of Christianity they practised, you see. Not here in Wales, however....
"Organised" paganism is an interesting thought. I'm not sure how much it's ever been an organised religion in the way that other religions are organised - there are, for a start, many different varieties of pagan beliefs and traditions.   I'm also curious about the way you think the Synod of Whitby caused the "re-emergence" of Christianity in these islands. Melvin Bragg has written an interesting novel about those times, called "Credo" - you might find it an informing read.

However, it comes down to this: I've been repeatedly referring to a living tradition held within at least one family that I know. You haven't met them, clearly. You want to know if their knowledge of a living tradition is "simply what they believe" - whatever that means, or if it's based in something we would all believe if we saw the evidence - what evidence, Les?   How would you "see" it? It's a set of practices, stories and ways of seeing the way the world works. When Ron Hutton met my friend, all of us present were rendered utterly speechless by the rude and overbearing way he treated her. Others attempted to let him know that here was a person with a genuine living tradition in her family - he made no attempt to ask her any questions at all, just laughed and said she was "prime source material" and then went on saying that he would only ever deal with written evidence.

So the book you're relying on is written by a man who had the opportunity to question "the evidence" I'm talking about but who made no attempt to do so. You yourself are continuing to dispute what I'm saying and all I can work out about your objections is that you haven't come across it yourself and therefore don't think it can be right.

I'm happy enough to leave it there. It doesn't really matter to me whether or not you believe I have a friend who knows a lot of stuff that has never been written down (it's not a belief system, by the way - belief doesn't come into it). You have, however, come around to saying almost exactly what I started off saying about the reason why traditional winter solstice songs probably don't exist as such.

If you have any specific questions about my friend and her traditional knowledge, by all means pm me, but it's rather off topic for the thread title.

Anne