Was residual animism partially responsible for Hitler's rise?

I would say that the opposite would be true. The German anti-Semitism was firmly rooted in good old Christian anti-Semitism. What it made the German anti-Semitism special was that it also targeted those who converted to Christianity, but it did so by claiming they only paid lip service and that they were still Jewish.

Partly Responsible? No more "responsible" than dozens of other social, cultural, economic and political factors

While Forsythe's assertion as written is piece of artistic license, there was an association of pre-Christian symbolism, as reflected in such cultural icons as Richard Wagner's operas featuring pre-Christian German legends such as Der_Ring_des_Nibelungen.

Cultural nationalism had been a factor in the previous century's establishment of the German Reich (Bismarck and the Kaisers). Hitler wasn't doing anything new, he was building on what Bismarck had managed about a half of a century before Hitler tried his hand at establishing a long lasting Reich. Cultural nationalism was one of his many themes used for political purposes.

... in the early phase, cultural nationalists worked to recover or re-invent traditional cultural stories in order to argue for the importance of their people’s cultural experience. Then they used this unified canon (an established past) as a point to rally their people (an activist present) to forge a united nation (a proposed future). We see this pattern in Wagner as well.

Hitler and his party appealed to (among other things) nationalism in their efforts to take Germany in their political direction. FWIW, Wagner's legacy has in the last half of a century certainly come under fire, in part due to an association with nationalism and anti Semitism, which is also associated with Hitler and the Third Reich.

Your question suggests that one should consider the social context when that novel was published.

I read The Odessa File shortly after it came out. (Early 1970's.) At that time, the hunt of for some of the Nazis who had escaped to Argentina, Brazil, and elsewhere was alive in the Western context. It was also in the news now and again as various SS or other sorts were found.

This was an era when WW II movies were still very popular (The Longest Day, Raid on Rommel, the Dirty Dozen, the Boys from Brazil were all contemporary films to the novel's release). The Nazi was a standard trope-villain in both film and literature. (Robert Ludlum featured a few Nazis as the bad guys, or shadow bad guys, in his books, also popular at the time).

Given the time of Fortsythe's book's publication, his alluding to that symbolism -- the pre-Christian Germanic Volk and their legends/paganism -- is not a surprise. It was par for the course in that time and place for fictional treatments of the Third Reich. Given the sales of the book, and the movie after, it was part of a successful formula used by Forsythe and others.

Is this literally true — that paganism/animism, residual from before the spread of Christianity, was partially responsible for the German populace's receptivity to Hitler — or is it a bit of invention?

No, there was or is no real residual paganism, if by residual you mean that there's some unbroken continuity between pre-christian belief systems and modern pagans

Or perhaps somewhere in between: it's not literally true as stated, but somehow metaphorically true?

Something like this: Romaticism in the 19th century had a strong streak of romticizing pre-christian culture. This ties in with later antisemitism, where progress and liberalism where seen as a bad, corrosive influence on the pure German people and associated with the jews. This is the type of thiinking found in the antisemite work 'The protocols of the Elders of Zion'. So far, we are not talking about a solely German phenomenon.

Starting in the late 19th century, you had several occultist far right organizations like the Germanenorden and it's follow up, the Thule Gesellschaft (the latter used some symbols later to be used by the nazis, like the swastika).

What is important is that these groups and other occultists did not have any direct coontinuity with pagan customs. Instead, we have (mostly) well to do folks with a christian education. They are somehow unconfortable the way western societies are developüing, and look to an idealized past.

While this kind of anti-modern thinking, clad in pagan or pseudo pagan prose was (and is) part of nazism (and other fascisms, look at Julio Evola for a prominent thinker along similar lines), it would be wrong to attribute Hitler's rise to power to it. This kind of pseudo-paganism was always a fringe phenomenon.

Continental Germany in fact converted to Christianity about the same time as the Anglo-Saxon peoples in England. It was only the Nordic countries, and some Eastern European ones, that came to Christianity significanly later.

So any residual paganisim is just as likely to exist in the (English-speaking) author's own culture, if not moreso.

Generally, I think the entire quoted passage is an attempt to distance the more repellent actions of wartime Germany from the author's own culture. It's all about the author's own insecurities, and has nothing to do with actual German culture.

The thought of a person much like oneself commiting atrocities is something a lot of people can't handle, so they have to find ways to make the perpetrator different somehow. The truth is there is nothing particularly special about Germans that makes them more likely to commit atrocities than your typical middle-american, African, Asian, Southeast Asian, or anybody else. We are all the same species, and we all have it in us.