I am saying that anti-semitism was well established and a part of european culture centuries before Muhammad was born or there were any muslims.
Since the OP has basically asked for the root cause of hatred towards the jews.
Then we must look at christian europe and not arabia.........
One can ONLY do that if one does not know about the problems that The Prophet himself had with the Jews of the Medina.
But your point is largely correct, I think.
Often (depending on what time and place you're talking about) Jews thrived under Moslem rule in ways they did NOT under Christendom.
Of course they were second class citizens in most time and places, but then too so were most non Moslems living under the yoke of Islam.
As were most NONChristians living under the yoke of Chistendom.
Such was the TYPICAL behavior of all Abrahamic religions when they were in charge.