Otherwise why do they care that the city of Yerushalayim is opening a parking lot on Shabbos? There is chillul shabbos in Yerushalayim and there will be whether or not the city opens the parking lot on shabbos. The עדה החרדית would not protest in NYC if Mayor Bloomberg (a Jew) opened a parking lot on shabbos who why should they care about Mayor Nir Barkat? After all, according to them the government is illegitimate and assur.
R' Amram Blau (a famous kannoi) once came back from an anti government demonstration and told the Brisker Rav how he laid down in front of the police cars to prevent them from going. The Brisker Rav said that he sees that R' Amram is also a Zionist. R' Amram was very puzzled, how was he a zionist? The Brisker Rav answered as follows. He asked R' Amram would you have laid down in front of a police car in Communist Russia? R' Amram answered no, I would have been afraid that they would just run me over and kill me. The Brisker Rav said that is the answer. You clearly believe that the zionists are better then the communists and would not kill you. That makes you in some small way a zionist.
The same point can be made today. Even the עדה החרדית understands that it is bad for the Jewish government of Yerushalayim to be מחלל שבת. As the Brisker Rav told R' Amra, Blau, they have bought in at least a little to zionism.