This is why comparing antisemitism with islamophobia is like comparing apples with pears. Actually it's not even that close since they are patently both fruit. Jews can only be Jews if their mothers were Jews. Curiously Jewish fathers pass on tribal hebrew names to their sons, which is why 'marrying in' is so important to Jewish traditionalists. The Jewish race relies on Jewish women passing on Jewish genes, not the fathers. Of course, for pure Jewish racial genes to be inherited, both parents need to be Jews. But according to the deeply unscientific Jewish laws, genetically only your mother counts. I suspect this was because Jewish laws were largely written to instruct how Jewish men should behave (wives being possessions). Consequently they were informed that if you married a non-Jew, your children could not be called Jews. Hence the necessity for your mother to be a Jew otherwise you can't be one. It was pointless legislating what happens if your father's not a Jew. Non-Jewish men wouldn't bother with Jewish laws anyway. Of course Jewish girls had to marry Jewish boys. It was traditionally the decision of the girl's parents anyway.
My mother is a Jew so I'm a Jew. I (very happily) married a shiksa (derogatory Yiddish term for a non-Jewish woman. In fact, and it says something about Jewish attitudes to the 'non-chosen', I don't think there is a non-derogatory Yiddish term for a non-Jewish girl). This means my three children can't be Jewish although they can follow the Jewish faith if they so choose (although quite what the appeal might be to outsiders is mysteriously more obscure than the possible appeal of Islam and Christianity). Clearly it's a race and not a religion - although you can adopt Jewish religious teachings and traditions if you want. In fact I don't personally know a single Jew who is in the slightest bit religious. Indeed I've sometimes heard even Rabbis declare they're not sure there's a divine mystical being.
Jews might follow the odd (and I mean odd) tradition such as not eating pig meat, but in my experience that's usually because of some deep-seated suspicion that the ancient ones thought they knew something about health and hygiene which had somehow escaped our subsequent progress into materialism and cheap food. As an aside, the reason semitic peoples (including Muslims) don't eat pigs is because as wandering middle-eastern tribes they simply couldn't take pigs with them. Unlike hoofed animals like sheep and cattle, you can't drive pigs. So it wasn't about them being unclean it was simply that it distinguished wandering tribes from sedentary ones. Jews didn't eat pigs because they couldn't keep them. Therefore traditionally those who did farm and eat pigs weren't Jews. Bet they would have if they could have. Bacon butty. Yum.
So antisemitism is irrational racial hatred born from some sort of deep genetic and tribal fear of others. Muslims, Christians, religious Jews, Buddhists etc have all made a decision to follow whatever brand of faith they fancy or are told to follow. People 'hating' Islam or Judaism etc, are expressing opposition towards belief structures and not the people who hold those beliefs. People who hate Jews are racist. People who hate Muslims are picking on what Muslims believe to define them, not, strictly, their parentage - although sadly it does tend to follow thanks to a form of mental child abuse where children are forced to believe in something that can't be proved and therefore ought at least to be open to questioning in order for them to decide, when they are able, whether to adopt the beliefs of their parents or not. I take my hat off to people who decide to reject the orthodoxy of their parents. It should never be such a big deal for anyone.
It is interesting to consider what is happening in the 21st century where a revolution in transport and communications within the past century has all but eradicated tribal influences such as religious allegiance except in regions where escape to the outside world, both physical and virtual, is restricted. This is either because of poverty resulting in a lack of resources and facilities to enable travel and dispersal of families and young people, or because of restricted access to world communications, especially scientific education, again either because of poverty or because of local censorship such as those practiced in strict Islamic countries and other heavily censored states. The net result is a massive and unstoppable rejection of religion by every developed nation except the USA. My guess is that this is because churches are big businesses in the USA. They compete in every community for congregations. Religion in the USA is literally heavily sold, unlike everywhere else where religions rely on subtler forms of persuasion as well as historical infra-structures including old church buildings and mosques which attempt to 'lord' it over the locals. This tactic no longer works. Money (mammon) talks loudest.
Intriguingly since the tradition of 'marrying-in', ie choosing a Jewish partner, is also disappearing fast, one might assume that the Jewish race will also eventually disappear. And since few people ever convert to Judaism (read this), it's all down to whether children born to Jewish mothers and non-Jewish fathers a) know they're born Jews (see above), or b) want to be identified as Jews. Few would aspire to be a Jew these days thanks to the bad press an arrogant Israel seems to crave. So although Jewish mothers will continue to officially produce Jewish girls to continue the race, more and more of those will 'marry-out' and abandon the tradition of passing on the bloodline and the traditions that go with it.
Another misconception is that there are approximately equal numbers of Jews, Christians and Muslims on Earth. There are in fact around 1,500,000,000 Muslims, 1,000,000,000 Christians and only 14,000,000 Jews - or about 100 times more Muslims than Jews. Hitler killed about 1 in 3 Jews alive at the time.
But despite his help, both the Jewish faith and the Jewish race are doomed to disappear thanks to 'marrying-out' becoming the norm. Personally I'm all for us behaving as a single species without artificial divides getting in the way of collectively solving far more serious planet-wide issues. So murderous anti-Semites can all calm down. We're doing the job for them.