I do wish you could become the "pet" of a Fallen Empire. Like, not just the awakened ones, the ones you start next to.
Xenophobes (what you meant when you said militarist) should want to make battle-thralls (Ur-Quan style) out of nearby xenophobic/militarist/authoritarian empires (allowing you to settle the juicy worlds that are near to the empire, but requiring you to occasionally go to war with other empires also in the vicinity that aren't thralls, cleansing their worlds) that they use as buffer states to keep the more vile races away.
Xenophilic ones should should want to have as many empires as possible under their "guidance" (read: some sort of pseudo-alliance/federation where the empires have automatic migration treaties together to go with the "xenophilia" thing, at least if your ethics allow it. If they do, you can't not be part of the migration treaty, you accept everyone even if they're All Bad Traits)
Materialist should want to keep an eye on your research, while offering some scraps of help along the way when they see you stumbling around in the dark like an idiot (so like a (x)% research boost while outright preventing you from researching dangerous tech)
I'm not really sure what Spiritualists should want... There's not really much that spiritualist does in-game that would really be worth equivalent trade-offs. Happiness/unrest-reduction boosts, but can't use AI? That's just what the trait does. I think if they ever expand upon religion in game, allowing your empire to have a specific faith (as opposed to just generic "Like, what if the universe was aliiiiive, man?") then that'd be something to work with. After all, Saudi Arabia and Iran aren't exactly best of friends, and they'd both be Spiritualist empires in-game, to one degree or another. You should be able to really REALLY hate other spiritualist empires, even more than materialist, because Burn the Xeno Heathen. Calling crusades for spiritualist militarists, evangelizing for xenophilic, etc.
If that were in, then I'd say a spiritualist thrall should be required to convert to the Fallen Empires religious viewpoint. Depending on how they'd work religions, that could be good or bad. If it was just "Same/Heathen/Heretic" traits, then it'd be good or bad depending on what you wanna do; You'd share religion with fellow thralls (and ex-thralls, and anyone who's been converted but not thralled) so you get a diplomatic boost but then you can't crusade them.
But if it were sort of Civ 5 style, where you create a religion with various bonuses (Paradox in Stellaris doesn't seem to like maluses, so I doubt there'd be any trade-off choices beyond "If I take this bonus, I can't put that other one in this slot" a la Ascension Perks) then it could ALSO be good or bad, though more than likely bad; A religion with bonuses you control is inherently going to be better for you, for what you want to do, than a randomly generated FE religion (even if it's a different generator for FE religions to combat that inherent bias, so that they get bigger bonuses, it still won't be tailored to what you need; Like if you were going for the crusade style, a religion you might make could have bonuses to happiness when at war with the heathen; A FE religion could instead just give you something like "Ascetic virtue" where your consumer cost is reduced/more mineral production. Still good, and the bonus could be more for the FE generated religion than if you took it for your own bespoke faith, but it still wouldn't be *as* good as the production boost from happiness from constant war, f. e. That kinda thing depends on how they'd balance them.***
Because of all that and the "Good or bad depending on context," I'm not even sure what kind of secondary effect you should get, or even if you should get one, from submitting to a spiritualist empire. Should you be outright prevented from colonizing holy world, instead of warred on when you do? Should you be allowed to colonize them, as sort of a bonus for allowing your people to convert? Should you get some sort of bonus to happiness, for "finally finding the Truth as laid down eons ago," or a malus for "forsaking our traditions"? It's hard to tell.
*** (Like 10% less goods use for asceticism, 30% FE Asceticism, and a 20% boost in happiness for heathen-stomping, assuming 75 pops on 5 worlds working an average games 100 year mark minerals (that's usually about 200? per month in my pre-Utopia games) then that would work out to 153.75 consumer goods baseline, 138.4 Ascetic, and 107.6 for FE Ascetic, compared to Space Deus Vult (assuming it causes all your pops to go from baseline happiness to the 20%+ production happiness, which while not impossible, is highly unlikely to work out that way, but it makes the math simpler) would increase your production to 240 minerals, assuming they all come from pops. (also unlikely, and also doesn't include energy, food, and research bonuses of 20%) It's a close call but for these numbers it would go to the FE religion; It wouldn't always, though. If you had more minerals from pops, or required less consumer goods, or had a large number of research labs/energy facilities, it might swing towards your own religion. Hell, because I didn't math the energy/food/research bonuses, it might already swing towards your own religion! It probably would, depending on if you need more research speed or if you need more minerals to pump out infrastructure and fleets.)
On another note: I'd love to see Fallen Empire use the three ascension paths, as a subset of them. Materialist = Synthetic Ascension, obv. Same as Psionics = Spiritualist. Not sure if Xenophilic would really fit as the biological one, though... The obvious fit is also materialist, and Xenophobe should want to stay as Perfect as they've always been (i.e. no chance of being ascended)
Ah! I got it. Xeno-(x) should stay natural as befits their "We Are Perfection" and "All Life is Special" stances, Spiritualist and Materialist should use their obvious ones, and they should allow some FEs to spawn as Hive Minds who may also be biologically ascended. Perfect fit!