I don't know the background for sure, but I've been told it sprung from an attempt to "purchase" converts to Islam. In Israel religious schools are state funded and some social programs are demonination based, so an increase in Muslims, for example, would likely result in an increase in state funding to their institutions. Whether that was the reason, I don't know. There was also an anti-proselytization law introduced in the late 90s which went nowhere. Some people confuse the two.
"There was also an anti-proselytization law introduced in the late 90s which went nowhere."
I believe one of the reasons the current 1977 law is rarely if ever enforced is that it could be challenged on grounds that it violates the guarantee of religious freedom as set forth in Israel's Basic Laws.
There are credible reports from many church affiliated and human rights groups concerning the harassing of Christian educational and charity groups in Israel, including but not limited to beatings, threats, destruction of buildings and other property, such as Bibles, commentaries, tracts, etc. Such activity, when carried out against Jews in countries like Russia and Germany, used to be called "pogroms." The authorities in those countries looked the other way, just as the Israelis reportedly do today.