By your own assertions, there is absolutely a contradiction.

If outsiders recognize the Jews' "well-known unscrupulousness" then they must recognize it themselves, and know they can not trust other Jews. Therefore in-group loyalty cannot exist because they know their trust will inevitably result in betrayal.

This is the magic of antisemitism. No matter what the facts, you can contort your reasoning to blame the Jews for anything, even if it's demonstrably nonsense.