This is not an endorsement of Likud, but rather a correction to your statement. Under the first government of Yitzhak Rabin in the 70's, the "Moslem Brotherhood" was allowed to operate as a charity among the Palestinian population. This was in fact viewed as a way for funding to enter the territories from King Hussein, which funded the organization's charitable activities, rather than from the PLO. It does not mean that Israel tolerated the political or military wings of this organization. Another thing you are forgetting is that as a result of the Camp David Accords with Egypt in 1979, Israel made a commitment to Palestinian political autonomy. The way they did this was to nurture the 'village movement', i.e. strengthen the mayors of the West Bank towns who were loyal to King Hussein. They did not tolerate openly Islamist politicians, and your allegation that Israel tolerated the military wing of Hamas is well-placed in the conspiracy world cosmos.
We want Iran cooperation, not meddling, Gulf Arabs tell Kerry (Reuters)
from the article: We need a Nasrallah