I have first hand experience with this "law" in Israel. We had to leave the country in order to marry because it was forbidden to marry a Jewish women. So we married in Cyprus in a secular ceremony directed by a Greek-orthodox - which neither of us is. Back in Israel, we were the lucky ones as an unwanted "mixed" couple since my Jewish wife fulfilled the conditions of the matrimonial ethnic fixation. At least our kids were not openly harassed and could go to school. Some of our brave friends had relationships in which the woman was not Jewish. If the wife is not Jewish, harassment by Israeli 'secular" authorities knows no limits, even if the marriage took place abroad. State and local authorities "lose" all kind of documents, permits and more. It's ridiculous since the countries in Western Europe and the US have smaller religious/ethnic minorities than Israel (over 20% non-Jews), but protect theim and grant them equal rights.
First refugees travelling on Hungarian bus arrive at Austrian border (Reuters)
from the article: Government to support non-Jewish civil marriage law