I've seen mention on a few websites that Birch trees are sacred to Freyja and Frigg but list no sources beyond "in Norse mythology" or "according to Norse mythology".
Is there any truth to this or is it just modern day associations?
It seems to be “modern day associatons.” Of course, demonstrating a lack of evidence is difficult, and I might be missing something, but the burden of evidence is on the person who says it. If you’re sincerely interested in knowing where they got it, I’d ask the people who run those websites, and if they can’t produce an answer, or send you off to someone else who also can’t produce an answer, I’d stop reading them.
This post does a pretty good job of laying out the evidence. I’m not gonna bother commenting on some of the ridiculous stuff that the author managed to dig up, I assume my readers don’t need me to tell them that "Nerthus split into Freyja and Hel” is not something worth arguing. One thing that's missed is that in the Icelandic rune poem, bjarkan ALSO doesn't mean 'birch,' though the word is certainly derived from the word for 'birch.' In the earliest written Icelandic rune poem, it's actually glossed abies which is the Latin word for the silver fir tree.
There is a theory about the Norwegian rune poem and its confusing second lines of each couplet, that says these second lines are mnemonics for remembering the shape of the rune. The theory, as articulated here by Jonna Louis-Jensen (link to PDF), holds that the bjarkan rune's shape is compared to the profile of a pregnant person, but that in this case the person is Loki.
I think one of the major vectors for this association is the conflation of Frigg with other goddesses (or proposed goddesses) from elsewhere in Germanic-speaking areas, such as Berchta/Perchta. By conflating Frigg with Berchta, Frigg inherits the association of Berchta and birch that, as far as I know, is entirely etymological, as both Berchta and birch were ultimately derived from words meaning 'bright' (though there was surely a great deal of time in between those derivations, it does seem reasonable to me that a perceived relationship between *berk- 'birch' and *berht- 'bright' could be maintained by Germanic speakers).
The above post mentions and links to another post about Vercana already, but I'll summarize. She was a deity worshiped by speakers of a Celtic and/or Germanic language whose votive stones appear in Roman Germania. Carl Marstrander thought that this was an attempt to write a Germanic *Berkanō, because Germanic *b is believed to have sounded like a "v" in most positions. If the name were *Berkanō, then we would expect this to be a birch goddess, but this is a misreading, because Germanic *b is pronounced like a regular "b" word-initially, and because other similar inscriptions have no trouble representing Germanic *b with Latin "B" (random example: Gabiabus). The weight of evidence demands that we read the stem of her name as *Werkan-. See here for more secure theories about the name. But you might notice that **berkanō persists in rune circles, supposedly the Proto-Germanic name of the b-rune, though this is incorrect (*berkaną is the most correct according to the little evidence we have, Ólafr hvítaskáld's grammatical treatise). Anyway, this theory seems to have contributed to the idea of a Germanic “birch goddess” generally, and made it easy to slide one or another goddess into that archetype or just cause some sort of “association”-seepage.
I suspect that ideas about a "birch goddess" got embedded into the common store of ideas about the runes and that this helped it proliferate. Associations between birch and birth are common but seem retroactive and ad-hoc to me, and I can't really trace them, there doesn’t seem to be anything to connect them in Old Norse. But taking it for granted that people have associated birch trees and birth, it’s quite easy to associate Frigg with birth and motherhood for a number of reasons (her relationship with Baldr, her answering the prayer of a woman unable to conceive in Vǫlsunga saga). Frigg has often been associated with the b-rune by modern rune people, probably because of some invented perception that runes have to be associated with a god, and none of the other ones being obvious matches.
I don’t expect that the relationship between birth, birch, and the b-rune was invented by nazis but they certainly had a hand in proliferating it. Völkische mystics actually severely downplayed the b-rune’s association with birch, sometimes failing to mention it at all (the Armanen name is bar, not obviously related to birches, and easier to fake a linguistic connection to birth). This probably preconditioned the people who took up their work and brought it into Anglophone popular rune magic (and reconnected it to birch). Michael Howard said the rune had to do with “the birch tree and the fertility rites of spring,” Athene Williams’ description is similar, and then the more immediately relevant ones to heathenry (Thorsson, Aswynn, etc) are in the post I linked in the beginning here.
The only sort of “association” I can find for birches in Old Norse comes from a fairy tale, part of which involves people being asked what kind of tree they would rather be. The cook said “birch” because it’s the best wood for a cooking fire. In Urglaawe, Frigg (Fried) is associated with birch, I believe mostly because of her association with the hearth, and with birch’s distinguishing characteristic of being excellent for burning. As best as I understand it, Urglaawer consider their version of Fried to have developed and acquired associations over the most recent centuries. Although even then, in Urglaawe birch has associations with a variety of things including other goddesses as well.
I’m shocked that I haven’t seen anyone try to argue that the bjargrúnar ‘saving-runes’ in Sigrdrífumál which are meant to help with delivery of a child are actually *bjarkrúnar or something. That the route I would have taken if I wanted to fake an argument.
If anyone else knows of something I’m missing feel free to say so but I don’t see a reason to believe this is anything other than a recent invention. As always I don’t really care whether people think it makes sense to them personally though I do encourage questioning any time the things that just make good sense to you happen to align with things that just made good sense to Nazis even when it’s mundane and seemingly harmless, especially when it involves ideals about women and giving birth.
