Nowadays there is no way to do a civil marriage in Israel, as the only authority for the marriage of Jews in the country is the Rabbinical Court. Unfortunately, the Rabbanut does not currently have LGBTQ wedding options, including people on the trans spectrum who have undergone external gender reassignment procedures and are in the Ministry of Population records.
In the past, there have been cases of couples where one partner was on the trans spectrum and they got married through the Rabbanut. However, once their trans identity became known to the Rabbanut, the marriage was annulled.1https://www.mako.co.il/pride-weekend/Article-36a888569f29e41006.htm
Common-Law Marriage
To receive rights like those of a married couple, you can choose the status of common-law marriage2https://www.kolzchut.org.il/he/%D7%99%D7%93%D7%95%D7%A2%D7%99%D7%9D_%D7%91%D7%A6%D7%99%D7%91%D7%95%D7%A8, though this solution does not give all the rights of a married couple3https://he.wikipedia.org/wiki/%D7%A0%D7%99%D7%A9%D7%95%D7%90%D7%99%D7%9D_%D7%A9%D7%9C_%D7%96%D7%95%D7%92%D7%95%D7%AA_%D7%9E%D7%90%D7%95%D7%AA%D7%95_%D7%94%D7%9E%D7%99%D7%9F. This is also a more fluid status, less well-defined and harder to prove than civil/religious marriage, and is less recognized by various bodies and often results in legal battles to receive rights.
As of today, you can sign up for common law marriage and receive benefits and municipal services similar to those of married couples in the following cities: Givatayim, Tel Aviv, Kiryat Bialik, Givat Shmuel, Ramat Gan, Rishon Leziyon, and Haifa.
Marriage Abroad
Another solution is to get married in a country that allows LGBT marriage, and then to sign up as a married couple in Israel with the Population Authority.4https://www.kolzchut.org.il/he/%D7%A0%D7%99%D7%A9%D7%95%D7%90%D7%99%D7%9D_%D7%97%D7%93-%D7%9E%D7%99%D7%A0%D7%99%D7%99%D7%9D
Despite the ban on civil marriage in Israel, LGBT couples that got married abroad can change their status with the Population Authority from “single” to “married”. However, being registered with the Population Authority does not give LGBT couples the rights of heterosexual and cisgender married couples.
Divorce of couples of the same sex that got married abroad and registered in Israel as married is done through the Family Court system.
Domestic Union Cards and Alternative Ceremonies
In Israel, there are several options for alternative Domestic Union Cards with legal standing.
This is the work of several organizations, such as New Family Organization who provide Domestic Union Cards with legal standing that give financial rights almost identical to those of married couples – whether to heterosexual couples or LGBT couples.
Another organization that offers alternative marriage ceremonies is Havaya – Israeli Ceremonies, who organize secular marriage ceremonies with an Israeli spirit, according to the needs of the couple. The Havaya organization also has a legal division that offers meetings regarding anything about marriage rights, different types of marriage agreements and financial agreements, and general advice about documents that it may be recommended to sign.
For in-depth reading about LGBT rights regarding marriage on The Association for LGBT Equality in Israel website.