Obviously, there are things that are higher priorities than arguing on the Internet. A message is not automatically owed a response. Still, the problem, is how those other places you cited offer no evidence to support your claims about Ra. One is just a non-scholarly source making a claim without evidence, and the other, while a scholarly source, doesn't say anything that supports your claim, at least none that I could find, and indeed the fact it doesn't would seem to diminish it (if there was such a tradition of bringing in palm trees to the home to celebrate Ra, wouldn't this scholarly article about the usage of palm trees and palm branches in religions, primarily the Egyptian religion, mention it?).
This is, unfortunately, very common in these sorts of things. People point to such-and-such custom of Christmas and claim it was co-opted by pagans. Setting aside the problem that there is frequently a very lengthy period of time between the alleged pagan custom and the start of the Christmas one (again, Christmas trees started around the year 1500, so we can be pretty sure they weren't taking it from some ancient Egyptian practice that had been dead for a very long time), often no one is able to provide evidence of the pagan custom to begin with.
If you are talking about the Chronograph of 354, it is certainly plausible, even probable, that "Natalis Invicti" on December 25 referred to Sol and thus was a mention of Dies Natalis Solis Invicti in its "Natalis Invicti". However, it isn't certain, and thus it is possible that the holiday's origin comes even later than that; that is an argument Stephen Hijmans (professor of Roman Art and Archeology), mentions in this article:
Usener's Christmas: A Contribution to the Modern Construct of Late Antique Solar Syncretism, in: M. Espagne & P. Rabault-Feuerhahn (edd.), Hermann Usener und die Metamorphosen der Philologie. Wiesbaden, Harrassowitz, 2011. 139-152
www.academia.edu
Regardless, the point is that
even if the Chronograph of 354 was referring to a celebration of Dies Natalis Solis Invicti, it also refers to a celebration of Christmas. It therefore provides no evidence of any celebration of Dies Natalis Solis Invicti
prior to Christmas. And if it didn't predate Christmas, then the whole idea that Christmas's date was taken from this other holiday collapses.
There is also some evidence, albeit disputed, for a belief in a December 25 going back earlier, possibly to the early third century or earlier (I wanted to post more on this, but unfortunately Christian Forums presently has some kind of bug that refuses to post my message if I include certain links). This is clearly prior to Dies Solis Natalis Invicti. But even if we were to disregard those and accept the Chronograph's mention of Christmas sa the first recorded instance, we still run into the same bottom line: We have no references to this festival prior to a time we know Christmas was celebrated. And if it came afterwards, as is certainly possible, if there was any imitation it would have been the other way around, with them copying Christmas.
