"So why would they have targeted Jews and not Muslims?"
Theology. Have you looked into it yet? The early Church Fathers' writings about Jews. The idea of keeping Jews alive but desecrated as a symbol of what Gd does to those who don't accept Jesus. It's not officially part of many Christian theologies now, but it was common & part of the relationship going back before Islam existed. My links from my research were removed when several sites rewrote themselves, so I'll leave it to you to find.
Here are some of the quotes:
http://restorationoftorah.org/SeedsofSeparation/SeedsOfSep1.html
What's notable is that scholars on the topic, state that the nastiest of the writing was typical polemic of the times. Also a lot of it is political competition under the arm of the Roman imperialism on who'd be beat up more. Then there was when Christianity became the religion of the Roman empire.
It was when it's use was continued for several more centuries, but without the political context of the Roman times (which were like this) that it was taken more literally & directly & viciously at Jews. Which is why the harassment of Jews took a while to get off the ground. It's as the Church took the words & the more & more literally as it developed totalitarian-style over it's own people (for instance not letting them become educated or read the bible themselves.)
Of course once put into action... the scapegoat tends to be targeted again & again as the known thing to target.
If you track antisemitism, it exists in places where Christianity took it. It does not match as well to where Jews are. It correlates best to where Xtianity has been in the past. Which is revealing. It's also been but differently, where Islam has been. Both of whoms theology includes references to Jews in a less than kind way.
----------
Also, Jews aren't obligated to have these answers. You are wanting to know why the harassers harassed, by asking the victims. We can dig for answers, but we dig by looking at the harassers' words, & have no more wisdom than anyone else on this outside of the harassers.
Have you found any answers? Do you have specific speculations?
If Jews had the answers & solution to respond to them - Jews would have. Jews have tried varied approaches. Some worked, others haven't. We know assimilation doesn't fix it, because German Jews were very assimilated more than Jews had been before -- right before the Nazis. (The Reform movement popular in Germany was in large part initially an attempt to be more like neighboring Christians in order to reduce being targeted.) We know religious dialog with Christian leaders has helped hugely, post-Holocaust when they were more open to addressing the "interrelational" problems.
There are a number of books on the topic, written by scholars with special research interest into the field. Have you checked into any of them yet? They'd know much more than people here.
-----------------
Were there a lot of Muslims in Russia proper, or was it in the Stans to the south? Those were more isolated, less developed regions that weren't integrated with the north Russia. Jews were in the major northern Russia cities, & put into shtels on the outskirts. So they were accessible. Muslims in the Stans at a time of slow travel, were "far away." Incidentally, they also didn't have a lot of antisemitism in the Stans among those Muslims from what I understand (by family that wound up there during the war).
===============
The Protocols talks about ME as though I'm evil. With all sorts of crazy ideas. I also find books that talk about blacks as inferior, offensive.
All that would make it inconsequential & a book I'd not think about -- if I didn't see real live significantly power politicans & leaders in Muslims countries, some in Europe restating & believing the sludge in the book as factual.
"I would personally find the print to be laughable because the whole context of it is just so blatantly absurd. "
From your brain... may it go to that of other humans.
The thoughts in it have been slung at me daily in YA. Also, more scarily, in real life, real incidents. It doesn't carry the emotion of absurd once it becomes dangerous. Then it's absurd AND offensive that someone would take it seriously & throw it at you in order to denigrate you. The whole Nazi idea that blues eyes are better, is the epitome of absurd. When it meant that Nazis were forcing darker eyed Jews to lick sidewalk filth with their tongues to humiliate them, then additional emotions happen, along with "absurd." In those emotions is, that they, their thoughts & behaviors are hateful. & that includes offensive.
---> Those words in the book are written to be denigrate, to lie about others, to steal their honor & integrity & replace it with hateful ideas about them.
(That's the crux of my answer. Wish I'd thought of it before I'd written the rest :). )
con't