Évelyne Sorlin: Cris de vie, cris de mort. Les fées du destin dans les pays celtiques. (1991) is an excellent source for this (although language and accessibility might be a problem). Évelyne argues that there is a Celtic tradition of the washers of the dead, and that this fit into the larger idea of those who dealt with the fate of humanity, including who was likely to live and die in battle. She also developed the idea of the banshee (which translated into female fairy) as a supernatural woman with a comb who mourns the dead. Like the washers of the dead who combed the hair of the dead and mourned their passing, the banshee echoes that role. See also Patricia Lysaght for the definitive work on this specific entity, appropriately titled, The Banshee (numerous editions).

The idea of the three Fates is widespread in Europe - whether called the Norns or the Weird Sisters - three women who wove the destiny of people. By extension, the Valkyries, women who gathered up the war dead, was a romantic extension of this core idea.

I believe you would be in error to maintain that this complex was in response to anything dealing with "gender in the Viking era." The complex is much larger than that single time and place.

I'm drawing here mostly on the stuff collated by Andy Orchard in the Cassell Dictionary of Norse Myth and Legend.

There is something about fate and women's roles in Norse culture, at least in the kinds of roles played in mythic stories and magical practices.

First, it's important that Norns and Valkyries aren't exclusive categories. Valkyries are "choosers of the slain" and Snorri Sturluson writes of them:

There are still other women, whose task is to wait in Valhalla, serve drink and take care of the tableware and drinking-vessels... these are called Valkyries. Odin sends them to every battle; they allot death to men and decide on victory. Gunn and Rota and the youngest Norn, who is called Skuld, always ride and choose the slain and decide on the killing.

In Voluspa, there's a Valkyrie named Skuld ("debt") and a Norn named Skuld, and Snorri seems to be trying to harmonize them by saying they're the same person. Whether or not they are, they're at least playing similar roles, selecting life or death and somehow dealing with souls in the afterlife.

There was a woman's role that seems related, and that's seid, "magic" or "prophecy," which could also mean a kind of sorcery based on messing with someone's fate. This is something Odin learned (and seduced women with), but which seems to have been practiced by women (or by "feminized" men... mmmaybe). Snorri says:

But such dishonor was associated with this skill that men believed that they could not practice it without dishonor, and so they taught the art to the priestesses.

There's another passage where Snorri says it was fecund Freyja who brought the practice of seid from the Vanir to the Aesir. Voluspa has a woman named Heid - who may be Freyja in other guise - who uses this gift of fate-meddling to stir up trouble with the Aesir:

[She] knew the skill of wands, she practiced seid where she could, practiced seid in a trance; she was always a delight to wicked women.

The practice also shows up in other sources. I'll just quote Orchard here:

In the Icelandic sagas, particularly the Fornaldarsogur, seid is clearly the preserve of witches, who can perform transformations and prophecies through its agency, for example the transformation of Signy described in the legendary Volsunga Saga.

Now, Orchard isn't drawing the connection here between Fate and fate-worker, but the similarity in role - or at least in sphere of influence - seems self-evident. Seid means "cord" or "rope", as in something spun out of thread, which is also suggestive, though I think weaving is more of a Greco-Roman thing for fates to do.

One thing I'm curious about is if the idea of there being three Norns is strongly evident before Snorri, since he's writing after Christianity reached Nordic Europe and long after contact with the Romans (there were Varangians working for the Byzantine empire when he was alive, I believe). The Norns' names, Fate (Urd), Happening (Verdandi) and Debt (Skuld) seem to mean Past, Present and Future, so that might just be a parallelism based on our perception of time. But even Snorri says there's more than three individuals, when discussing Fafnismal:

There stands a fair hall under the ash [Yggdrasil, the World-Tree], by the well, and out of this hall there come three maidens, who are called Urd, Verdandi and Skuld. These maidens shape the lives of men; we call them Norns. But there are other Norns who visit every child that is born, to shape its life, and they are descended from the Aesir, others still are descended from Elves, and a third kind from the race of Dwarfs... good Norns, from a noble line, shape good lives, but wicked Norns are to blame for those whose lives are miserable.

(Emphasis mine.)

Anyway, I suppose the real question about gender roles is whether seid-workers were mostly storybook witches or more often real-life oracles. Orchard doesn't get into this, but The Saga of Erik the Red does describe a seid-worker, so there were probably at least some who existed outside the stories, working as diviners or even some kind of trance-performers. The archaeology is pretty slim on that, though, as far as I know.

(Edit because capital letters are hard, especially on a phone.)