The simplest way to answer this question is to see how much support Judaism has in Islamic countries (not much). The more likely cause of anti-Judaism is that outside of Israel, Jews make up only a small fraction of the population, but often have a larger fraction of the wealth then their small numbers would suggest. This makes them an easy target for people that are hunting for scapegoats.
Christianity is not the root cause of anti-Judaism sentiment. There are other causes as well. Xenophobia is nothing new to the human condition and it is clear that other religions (namely Islam) have also been a root cause of anti Jewish thought. Hitler and his genocide against Jews is another example of anti-Jewish feelings that did not come from Christian ideology.
Christianity is not the root cause of anti-Judaism. There have been people who denied Judaism far before Jesus and the Christian faith was developed. If you read the Bible and Koran this is very clearly detailed in the Old Testament. Do a few Internet searches, these problems go back further than you are aware.
No, Christianity is not the root cause of anti-Judaism, because people and groups hated the Jews long before Christianity existed. It must have been rough for all those developed nations to lose in battle to the Jews all the time back in the Bible days. The resentment has just really never gone away. But that is not the Christians' fault.
I do not think that Christianity is the root cause of anti-Judaism. I think that to think such a thing is pretty foolish considering Jesus himself was a Jew. To be anti-Judaism is to be anti-Jesuse. I think that people need to realize that there are more causes to anti-Judaism than Christianity.