Whoo boy. Yeah. So I used to read the Dresden Files and that book was where I stopped in fact.
Soooo... let me start with a TL;DR and then get into details.
TL;DR: Waldo Butters is the epitome of Butcher's "Judeo-Christian" worldview--a token Jew existing in a universe of Christian metaphysics and ethics as a way to try to claim that, no, really, Judaism and Christianity are in complete agreement with each other!... when the only theological overlap between the two is that "fish isn't meat".
Expanding on this in the general context before I get to the specifics of Butters' character, "Judeo-Christian" is a popular term in Christian circles these days--ever since 1946, where it exploded in popular use for some reason--that attempts to paint a unity and commonality of history, theology and culture between Judaism and Christianity.
This is not the case, and hasn't been for centuries. Literally one of the first things the early Church did was jettison every bit of Judaic theology and practice it could, and spent the next 19 centuries calling Jews "Christkillers"--i.e. "the Jews were specifically and eternally responsible for the death of Jesus Christ". Put a pin in that, we're coming back to that later.
In the decades since the Holocaust, Christian persecution of Jews has taken a different form away from the old massacres, blood libels, legal discriminations, and other forms of "Jew-hate", primarily aiming at absorbing Jews via cultural osmosis and appropriation instead of the old way of "grab Jews and shove them in the baptismal font while they scream." What I mean by this that there's a two-fold approach going on, where there's an explicit, well-funded, and organized two-pronged strategy of erasing the boundaries between Judaism and Christianity with the intended goal of Jewish genocide--i.e. for there to be no Jews left, just Christians playing Jewish dress up.
Prong one is cultural appropriation, plain and simple. Saying that they "love Jews", Christians take everything Jewish--and I do mean everything, down to the foods--and say that they're about Jesus, and that they're "trying to get in touch with their heritage"... a heritage which is not theirs, and which they spent 80+ generations literally murdering Jews for practicing. But if they can appropriate it well enough... well, ask any neo-pagan these days how hard it is to get an accurate feel for how their practices were done before the monks and missionaries arrived.
Prong two is even more disgusting, somehow. Back in the 1960s, a bunch of Southern Baptists found that they were having a hard time converting Jews, whose conversion is required for Armageddon and the Second Coming. Their solution was to create a fake "Jewish" denomination that takes the appropriation I mentioned above and dials up the nob until it snaps off. Called "Messianics", they claim to be Jews who follow Jesus. Their theology is Christian, their ideology is Christian, and their religious trappings are profaned Jewish images, twisted with the name and idolatrous image of Jesus, in whose name literally millions of Jews have been slaughtered over the centuries. Not one actual Jewish denomination agrees with them, but they are incredibly well-funded by Christian groups, to the point of them having training programs for--and I am not making this up and will provide links if people want--deep cover missionaries posing as Orthodox Jews.
The point here is that a Jew acknowledging Jesus as their Lord and Savior is, by rare universal agreement among Jews, no longer a Jew, and we've been in agreement on this for close to two thousand years.
So now let's get to Waldo Butters and his place in the Dresden Files.
Now, the Dresden Files runs on Christian metaphysics overall. The universe is in conflict between Good and Evil, and that's even before getting into the very Christian points in the series, like the Shroud of Turin being the MacGuffin in book 5, or the Holy Grail being the object in a later book.
Jewish metaphysics are very different; we don't view the universe as being this grand battle between Good and Evil, period. Heck, even our ghost stories are legalistic and therapeutic instead of combative and antagonistic like the ghost stories are in the Dresden Files.
That's first off for the Dresden Files.
And then we have Waldo Butters... who is introduced as a literal walking stereotype--the nebbish. I've mentioned before that the Jewish masculine ideal is that of "Man as Scholar, not Man as Warrior", and Butters is the epitome of that... looked upon from the outside and mocked. He's small, physically unassuming, and primarily intellectual, and a physical coward. His character growth is becoming a warrior and fighter, culminating in him picking up one of the Swords of the Cross.
Now, in the Dresden Files, these are explicitly three magical swords, named for the three Christian virtues of Faith, Hope, and Love... with one of the Nails from the Cross worked into the hilt for each.
You know, the nails used by the Romans for the execution of a Judea rabble-rouser in whose name more Jews have been killed than any other, and who we Jews have drawn a hard line at worshipping on literal pain of death and torture for two thousand years?
Yeah. Those nails, and that god.
Butcher has Butters pick up the Sword of Faith in Jesus Christ, whose hilt bears one of the nails that was used to kill Jesus and for which Jews spent every Easter and Christmas for centuries hiding in our homes for fear of a screaming mob crying out for vengeance and sometimes hearing a torch thrown on the roof of that home...
And has the audacity to say that this man--whose Judaism is informed at best, who is introduced as a stereotype and is used as a token for "Judeo-Christian" brownie points, whose character development is directly away from the ideals that we hold as good--is still "Jewish."