The legislation is being promoted by Knesset Member Eliahu Gabbay of the National Religious Party. Previous rulings by the country's High Court have been against local municipalities being able to make decisions on religious matters however the bill changes the Basic Law so (from Haaretz)

    As such, it is very doubtful that the High Court of Justice could overturn it. In fact, the High Court has never canceled a Basic Law. The Court would intervene and quash such a law only after becoming convinced that it constitutes a threat to democracy

Clearly Haaretz believes that the High Court would not consider that the banning of peaceful protests or demonstrations on religious grounds would constitute a threat to democracy.

Last year when Jerusalem was due to hold the World Pride event, the full range of religious force was imposed to stop it. The Sephardic Chief Rabbi Shlomo Amar wrote to the Pope to enlist his help.

    "We were shocked to hear of plans to hold the world Pride Parade in the Holy City," rabbi Amar wrote, "The city which the entire world looks up to due to its holiness and glory, is now being attacked by evil people who wish to violate its honor and humiliate its greatness with deeds that theTorah despises, as well as all other religions. There is no need to elaborate about their plans and evil actions that bring humanity's dignity to the ground"

Ashkenazi Chief Rabbi Yona Metzger spoke at a religious meeting in Moscow.

    Metzger said: "As everyone knows, Jerusalem is the cradle in which the three monotheistic religions spouted. We have to unite to preserve its historical holiness and the values of purity and morality which characterize it."

Ynet report for above two quotes.

Yehuda Levin, a member of the Rabbinical Alliance of America went to Israel with the mission to stop the event. He told World Net Daily"Israel is the Holy Land, not the homo-land,". WND gave some more examples of this bigot's views:

    Like some other rabbis here, Levin believes that there is a direct correlation between the homosexual parade scheduled to take place in Jerusalem and the recent onslaught of rockets raining from Lebanon and Gaza.

    Citing Leviticus [18:22-28], Levin said the Torah relates to Israel' current conflict.

    Leviticus states, "You shall not lie down with a male, as with a woman: this is an abomination. For the nations, whom I am sending away from before you, have defiled themselves with all these things. And the land became defiled, and I visited its sin upon it, and the land vomited out its inhabitants. ... For the people of the land who preceded you, did all of these abominations, and the land became defiled. And let the land not vomit you out for having defiled it, as it vomited out the nation that preceded you.'"

    Said Levin, "The terrorists, the leaders of Israel's enemies are working for the destruction of Israel, to wipe the Jewish people off the map."

    Levin believes their efforts are succeeding due to what he calls sexual promiscuity in the land of Israel.

So it's not Hamas or Hezbollah that was responsible for last year's wars, it was the homos. That was actually quite ironic as the objections to the march came from Christian and Muslim clerics too. The planned event was cancelled but not after violence involving the fire bombing of synagogues. (In 2005  an ultra-orthodox young man wounded three parade participants with a kitchen knife at a lower key event.) Later in 2006 a fixed rally took the place of the march.

Already this year, in April a bomb exploded injuring a worker, believed to be the work of the same ultra-orthodox groups who rioted in Jerusalem last year.

    Unknown persons detonated a medium-sized explosive device near a peaceful vineyard by the Israeli town of Beit Shemesh early Friday morning.

    The bomb's location ran close to the path of the security fence being built just south of the town, near the Beit Jamal monastery, and a civilian tractor driver working at the construction site was lightly wounded in the explosion. An emergency medical team evacuated the man to the Hadassah Ein Karem Hospital in Jerusalem.

    Security forces investigating the scene later reported that they had uncovered leaflets at the scene of the crime which apparently call for the cancellation of the upcoming gay pride parade, set to be held in Jerusalem in late June.

Ynet

The way the law is framed, the Jerusalem authorities could ban the Gay Pride march but it is not clear whether it would also be used to stop the protest marches by the haredim which last year ended in  violence and police injuries.