To get legally married Israel, you have to satisfy the rabbis that both of you are officially Jewish by their lights. (Those who can’t or don’t want to bother typically fly to Cyprus to get married.) From YNetNews in Israel:

Experts on genetics and Jewish law say they found a ‘Jewish gene’ that could prove one’s Jewish roots; researchers have been studying mitochondrial DNA that one receives only from his or her mother, which they say could help establish one’s connection to Judaism.

Elisha Ben Kimon|Published: 28.05.17 , 15:52

A group of experts on genetics and Halacha (Jewish religious law), who are studying the so-called “Jewish gene,” are claiming that the gene can help prove one’s “Jewishness” in line with Jewish religious law.

“This could be a significant breakthrough,” explained Rabbi Yosef Carmel, head of the Gazit rabbinical court and the Eretz Hemdah Institute for Advanced Jewish Studies. According to Carmel, “Using a simple sample of saliva can save a long and difficult conversion process.”

Any person who wishes to be recognized as a Jew—for example, in order to get married in the State of Israel, which can only be done through the Chief Rabbinate—is required to prove their Jewish roots. In Jewish religious law, only those born to Jewish mothers are considered Jewish. Those who wish to be recognized as Jews have to provide proof of Judaism several generations back in the form of documents—such as birth and marriage certificates.

This can be a problem for over 400,000 people, particularly immigrants and especially those from the former Soviet Union, who don’t have the necessary documents.

People who cannot prove their Jewish roots are considered as “undefined,” with applicants having to undergo a long and tedious conversion process that quite a few wish to avoid and many do not complete.

Currently, the Eretz Hemdah institute is preparing an article to be submitted to the Chief Rabbinate detailing a Halachic-scientific breakthrough that claims anyone whose Judaism can be proven genetically is legally (in the Jewish legal sense, that is) Jewish.

“In recent years, (researchers) in Israel and in the world have been studying mitochondrial DNA—structures within the cells—that a person receives only from his or her mother,” explained Rabbi Dov Popper, an adviser at the Puah Institute, an Israel-based international organization that helps Jewish couples with fertility problems.