ChatGPT and Grok say Christmas either does or might have pagan origins, but not that it definitely does not have pagan origins (yes, I know "proving negatives"is very difficult†).
LLMs do very poorly at judging the truth of long-term myths. When something has been asserted confidently on the internet over a long enough period of time it becomes baked into the weights, regardless of truth.
I provided a source from a religious studies scholar on Christmas trees specifically (one of the most frequently-cited "pagan" traditions). If you can point me to something with similar provenance I'll read it, but I'm not going to waste time on LLM responses.
ChatGPT: https://chatgpt.com/share/676c8fd1-b6e0-8005-a86f-d43ac17634...
Grok: https://x.com/i/grok/share/8fQKIFO1WGl3nDVZ6uFaJmPTW
†Grok on proving negatives: https://x.com/i/grok/share/kcHkjqzJ5lx5kMyl4GL0nMuw3