Hell, I want to model a lot of US policy off of Israel because I think they are doing a lot of things wayyy better than we are, for example, not allowing gay marriage, and I respect them greatly for that.
In Israel, there is no such thing as civil marriage. Marriage is not only exclusively religious, but exclusively for the four Abrahamic faiths recognized by the Israeli government: Judaism, Christianity, Islam, and Druze. More specifically, Israel requires that both spouses must be government-registered members of a recognized denomination of the same religion; interfaith marriages are not permitted even if they are allowed by the religious faith.
For Christians, the recognized denominations are Roman Catholic and Orthodox. However, the law does not actually prohibit other Christian denominations; it merely does not recognize them. Since Protestant churches have no centralized authority which can coordinate with the Israeli government, Protestants who wish to be married in Israel must apply for government permission, which is granted on an informal, ad hoc basis.
For Jews, the only recognized denomination is Orthodox, and this is an absolute exclusive -- those of other Jewish denominations are explicitly not permitted to marry.
So Israel does not actually disallow same-sex marriage; if any of the recognized denominations of the recognized religions allowed it, Israel would respect that. It's simply that Israel only allows Abrahamic religious marriages coming from recognized denominations, generally those that are centralized enough to have official hierarchies and rulesets. Israel does not itself impose any restrictions other than not allowing interfaith marriages; all other restrictions are simply those of the recognized religious hierarchy.
Outside of this, Israel grants limited recognition of marriages performed outside of Israel as a matter of international reciprocity, and same sex marriages are included in this legal reciprocity on an equal basis with all other non-Israel marriages.