Early Christian anti-Semitism does not really deserve to be given a special label like that, as it suggests some kind of fixation on Jews in particular. Rather it was the standard in-group vs. out-group demonization, with a detail here and there about the out-group members used just to give it a modicum of plausibility, as in any Friend of a Friend tale.
For example, early Christians spread the rumor that Jews engaged in ritual sacrifice, cannibalism, incest, etc. -- but so does every group around the world when they're talking trash about the next tribe over. That's one reason anthropologists have trouble figuring out if some group really practices cannibalism or whether it's just a rumor from informants of a rival tribe.
What today would be called anti-Semitism doesn't look like it gets started until the Ashkenazim cohere as a group -- there are very specific claims about being good with money, controlling lots of money, emphasizing cunning and cleverness over morality, pitting two sides against each other for his own individual gain, viewing nothing as so sacred that it's beyond striking a deal over or profiting from, and so on.
I'm sure there are other less famous examples from a bit earlier on, but one of the first widely known examples of this type of Jewish character in European culture is Barabas in Marlowe's The Jew of Malta. A lot of his image and behaviors are stock, so late 16th C audiences must have already been familiar with this character. True, the character lives in Malta and so was probably not Ashkenazi, but it was common for English authors to project local action onto exotic locations. Marlowe seems to have the northern European Jews in mind.
Well that was way over there and way back then, right? Nope: I watched Aliens for the first time in awhile, and there he is again, even in a work from the modern post-Enlightenment age and in the most Semito-philic developed country outside of Israel. The Machiavellian sell-out / traitor has the laughably British name Carter J. Burke, but he's played by Paul Reiser's quintessentially Ashkenazi stage persona, no matter what movie he's in (like the neurotic Detroit gumshoe in Beverly Hills Cop). I guess there would have been a boycott if he had been named Max Lipschitz and had said, right as an alien was about to kill him, "Look, I know what you're thinking, but let's be rational and negotiate a deal here..."
That's at least four centuries of stability for this character type, and in elite and popular culture. Given how specific the type is, these portrayers must be picking up on something real. The over-representation of Ashkenazi Jews among Nobel Prize winners doesn't mean that the average one is super-brainy, but it still suggests that their average is above other groups' averages. And the social and economic ecology that Ashkenazi Jews were forced into and adapted to may not have required Nobel-level smarts, so it's not like the extreme values were selected for -- just the values around their average, where the person is smart enough to succeed as a tax farmer.
Similarly with Machiavellianism -- this may only represent a small minority of Ashkenazim, and this extreme value may not have been selected for, but it's hard to escape the conclusion that their average in this trait is higher than it is for their host populations, and that this fairly but not excessively Machiavellian level served a member well in the financial white collar ecology that they are adapted to.
I wonder if this is behind the unusually wide diversity of political positions that Ashkenazi Jews hold (they produced both Marx and Hayek -- oops, I meant Mises. I'd better not write so late at night...). If the average one is leaning in the amoral Machiavellian direction, that will reflect badly on someone who leans the other way, so the latter goes even further out of their way to prove their anti-Machiavellian beliefs to the host population. It's like the greater cultural diversity among whites in the south -- you see both rednecks and those who labor to prove their sophistication, lest they be mistaken for one of the bad white southerners. You don't see this so much where the whites are just bland and without embarrassing / bad apple leanings, say in South Dakota. Blacks who have been around lumpenprole blacks for a long time are more eager to prove, in the company of whites anyway, that they're not one of the bad blacks but educated and responsible. And a community-minded Ashkenazi Jew who through extensive personal experience senses the Machiavellian strain within his group will push even harder in the other direction when he's forming his beliefs.