There’s an XKCD that a lot of people have seen which plots most-played Christmas songs by decade of release:
The conclusion it presents, “every year, American culture embarks on a massive project to carefully recreate the Christmases of Baby Boomers’ childhoods,” is true in a sense, but mostly wrong.
The biggest problem with it is that it’s using radio songs. There are several problems with this; they are largely technologically constrained to not have been recorded prior to the 1940s because sound recording was awful back then. Having done a fair amount of swing dancing, if you ever heard a recording made from the 1930s or worse the 1920s it’s barely listenable. You simply need to get a modern band to play those songs now in order for them to not hurt your ears. On the flip side, there just haven’t been any good popular christmas songs composed since the 1960s because of cultural shifts, but that’s a different story that I’ll get to later. The really big issue, though, is that the radio doesn’t play the really popular Christmas carols, they only play things recorded by popular recording artists. Even where popular recording artists record traditional carols, the radio will play versions by all sorts of different people, so a song which gets a lot of play time will not get it all on the same recording. To have this sort of concentration, we need the songs to still be in copyright so there’s only one or a very few versions of it available for the radio to play.
To really see the point, consider the popular Christmas carols—the ones that people actually sing—and when they were composed:
Jingle Bells: 1857
Heark! The Herald Angel Sings: 1739 (current musical arrangement: 1840)
Joy To the World: 1719 (current musical arrangement: 1848)
God Rest Ye Merry Gentlemen: traditional; at least the 16th century
O Holy Night: 1847 in french; English version by a guy who died in 1893, so before then
Silent Night: 1818 in German, English translation in 1859
O Come, All Ye Faithful: 1751
What Child Is This: 1871
Away in a Manger: 1897
The First Noel: 1833
We Three Kings: 1857
So yeah, the first problem is that if you consider stuff that can’t really have been done prior to when the baby boomers were born, you won’t find it. In a sense we’re done; the only thing which is trying to recreate the boomers’ childhood was a thing that barely pre-existed the baby boomers (commercial radio in the modern format).
Christmas songs after the 1960s tended to be either novelty songs or songs that really aren’t family friendly. As people got less religious and more sex-obsessed and so sang about having sex on Christmas with various degrees of veiling their meaning. That’s not actually going to be very interesting when it’s competing with songs about having sex five times a day, so it’s not shocking that these haven’t been popular. (In short: religious people won’t like them and irreligious people can get better).
There’s another aspect, which is that there was a short time period, as popular culture was becoming hardcore secular, where the newly secular people could enjoy the religion of their parents without participating. That’s the sort of thing that only lasts a decade or two; after that the energy just goes out of it.
Here in 2021 I think that the secular energy for Christmas is fading fast; one of the more popular things for adults to do is to agree with other adults to not exchange Christmas presents because it’s just a pain in the neck. No one really likes getting together with family to eat dry turkey and too many store-bought pies—that’s why they only do it when it’s an obligation they can’t get out of—and the concept of universal good will just doesn’t make any secular sense and has been long-since abandoned.
The grain of truth to the XKCD is that there is an attempt to LARP the most recent sincere Christmas celebration anyone can remember, which happens to be the baby boomers’ childhood Christmases. That’s mostly a coincidence, though, and in any event it includes many things which pre-dated the baby boomers. Twas the Night Before Christmas was first published in 1823 and the general depiction of Santa Claus as dressed in red and white originated at the latest with Puck magazine in the early 1900s and was set in popular imagination by the 1930s with widespread soft drink advertising campaigns (most notably Coca Cola).
So yes, the baby boomers were influential. The world did exist before them, though, and they don’t explain most of it.