His Roman church eventually came around to worshipping the birth date of Sol Invictus, the 25th of December.
This narrative is refuted in
this paper which has a detailed analysis or Roman paganism and the history of Sol starting p281. There is no evidence that Sol was 'elevated' into some kind of henotheistic primacy as representations are consistent over centuries.
The idea that 25 Dec was a longstanding and important feast day for Sol Invictus has no evidence to support. The only source that identifies 25 Dec for Sol, also identifies it as the date of the Birth of Christ and is from the 4th C. Even this is ambiguous as it doesn't mention Sol, only 'birthday of the unconquered'.
Festivals for Sol are also recorded in August 8, 9, 28 and October 19, 22 and Dec 11, all predating the Dec 25 date recorded in a single source.
So there is no source that clearly identifies 25 Dec as a major festival for Sol. The one source that is possible also mentions Christ on 25 Dec. There is no clear evidence Sol was elevated into a position of primacy at any point. Festivals for Sol were more established on other dates.
This, the cult of Sol Invictus is overstated in its importance and the idea that there was a massively important festival in his honour on Dec 25 is not supported by the evidence.
Romans (and many others) did acknowledge cosmological significance in the equinoxes, although theses were not inexorably bound to Sol Invictus. These are tangible astrological events after all, not simply religious constructs.
As such, based on cultural perception of the equinox as significant, Christian dates became attached to these relating to both Jesus and John the Baptist because they were the equinoxes, not because they were trying to appropriate pagan festivals to win converts.
The similarity is likely based on the similar cultures rather than direct imitation.
