Hmm...anti-Semitic backlash in the U.S., maybe if Judah P. Benjamin manages to negotiate foreign recognition of the Confederacy or something like that?
This might lead to a more philo-Semitic Confederacy, especially if premillenial dispensationalism (the End Times theology that leads to many conservative Christians supporting Israel) becomes part of Southern churches.
In TTL, the Confederacy (if it lasts that long) becomes a supporter of Zionism, especially in the Holy Land and not in substitute sites like Uganda, while the U.S. defends the rights of Palestinians out of spite? And Jews might find the Confederacy friendlier than the North if there's an anti-Semitic backlash.
Perhaps TTL's American Jews might be more racist than OTL as a result of their mistreatment by a philo-black (to a point) society. This could even get theological, if they too start believing in the Curse of Ham or using OT rules about what ethnicities the Israelites were allowed to intermarry with to justify condemning interracial marriage.