Officially, Iraq does not have any Jews left, but as I discovered recently when I was invited to spend a couple of days with three families in the Kurdistan region of Iraq who are proud of their Jewish ancestry, the great-grandchildren of the country’s last Jews are extremely aware of their Jewish roots. The small minority of Iraqi Jews who had not fled to Israel due to antisemitism by the 1970s converted to Islam, or to a lesser extent, to Christianity. As a result, although there are large communities of Iraqi and Kurdish Jews in Israel, Jews are now invisible in Iraq itself.This does not mean they have disappeared completely. Although they keep silent about their roots, the families I met are very aware of them. One of the best moments of my stay was when they sat down to draw up a family tree in an effort to understand how they were interrelated.When we couldn’t find any paper, we used a piece of cardboard instead. Right at the top came the great-grandfather, a Jewish Kurd who married a Muslim woman and converted to her faith. Sitting on the floor of the sitting room, my hosts added his children, grandchildren and great-grandchildren and pointed out their own places on the tree.I was amazed by their knowledge – who knows the names of so many distant family members by heart? – and by their pride in the blood that linked them: the blood of their Jewish great-grandfather. They call themselves Benjews, which means ‘Jewish roots’ in Kurdish and is used for everybody who has Jewish ancestors. That Judaism only recognizes descent through the female line was of no importance to the men and women making their family tree. For them, it is simply about the Jewish blood they have running through their veins.In any case, the Jewish focus on the female bloodline is out of kilter with their own tradition, in which the male line is dominant. For them, having an ancestor who was Jewish means they are Jewish, too.So here are three Muslim families who treasure their Jewish roots. But not too openly (the cardboard family tree was put out with the trash after they had photographed it), because many strict Muslims would not understand. And in Iraq there is still a real risk of Salafi Muslims taking revenge on people who identify as Jewish and who they associate with Israel; people also fear the long arm of Iran reaching in from across the border. But amongst themselves, they proudly identify as Benjews and socialize together because of the ancestry they have in common.Most Benjews have no ties to the state of Israel. They are proud of their Jewish roots, but feel no less pride for their Kurdish identity. Politically, they simply feel Kurdish. If they admire the Jewish state, it may be because of Israel’s success in safeguarding its existence in a hostile world, which they consider as an example for the Kurdish cause. If they long to visit Israel, it will be to visit long-lost family members. Or for economic reasons, for if Israel opens a door that other western nations have shut, they might use it to emigrate to the West.Only a few Benjews still adhere to the Jewish faith. I met a woman who knew all the Jewish customs and prayers for the Sabbath; she had learned them from her mother. Others are interested in learning more about the faith of their ancestors – not because they want to live as Jewish believers, but because it is part of their cultural heritage. For they are Muslims, albeit with a Jewish bloodline and background. No one knows how many people like them live in the Kurdistan Region, but the number must be in the thousands. The one family tree the three families drew together involved more than 100 people over just three generations. But only some of those thousands are aware of their roots, with the young being more curious about their Jewish ancestry. I discovered this when word got out in Kurdistan that I had written a book about the history of the Jews in Iraq, and young Kurds started approaching me with questions that they had not been able to ask elsewhere about their Jewish roots.This group is not interested in returning to Judaism. They are a cultural minority within the Kurdish community and at the most demand conditions in which they can be open about their ancestry instead of meeting and gathering information about their heritage in secret. The recently sacked representative of the Kurdish Benjews made a huge mistake when he suggested appointing an Israeli rabbi as the chief rabbi of Kurdistan, as did the Minister for Religious Endowment when he actually appointed him. The chief rabbi wants to determine who is Jewish through their mother line, to educate them in Judaism, and set up a place for them to pray. But no one has ever asked Benjews whether they feel the need for it.From my conversations with Benjews, I am fairly sure it is not fear that is stopping them returning to Judaism. They simply are not interested, either because they see themselves first and foremost as Kurds, or because they are practicing Muslims. They are Kurds with Jewish roots, not Kurdish Jews. It might seem like a small difference, but for them it is all-important. Benjews are doing what they can to hold on to what is left of their Jewish identity, and would love to be able to come out into the open and research their history and culture. But appointing a chief rabbi will not help them toward this goal. Bringing Judaism back to a country where radical Islamic groups like Al Qaida and ISIS have flourished so recently can only be counterproductive. It will bring the Benjews peril not acceptance, and ignores the wishes and dreams of a group that has been living in fear for too long and which deserves our protection.The writer, a correspondent in Iraq for Dutch and Belgian media and various international websites, is the author of The Jewish Bride, a novel about Iraq’s Jewish heritage. It is available in English from Amazon.