Most Israelis just want the Palestinians entirely out of Israel and to be rid of the whole problem. They’re not particular about how that problem gets solved. From Megan K. Stack at the New York times via archive.is:

A barrier wall snakes along the West Bank.Credit…William Keo for The New York Times
It was the pictures of Palestinians swimming and sunning at a Gaza beach that rubbed Yehuda Shlezinger, an Israeli journalist, the wrong way. Stylish in round red glasses and a faint scruff of beard, Mr. Shlezinger unloaded his revulsion at the “disturbing” pictures while appearing on Israel’s Channel 12.
“These people there deserve death, a hard death, an agonizing death, and instead we see them enjoying on the beach and having fun,” complained Mr. Shlezinger, the religious affairs correspondent for the widely circulated right-wing Israel Hayom newspaper. “We should have seen a lot more revenge there,” Mr. Shlezinger unrepentantly added. “A lot more rivers of Gazans’ blood.”
It would be nice to think that Mr. Shlezinger is a fringe figure, or that Israelis would be shocked by his bloody fantasies. But he’s not, and many wouldn’t be.
Israel has hardened, and the signs of it are in plain view. Dehumanizing language and promises of annihilation from military and political leaders. Polls that found wide support for the policies that have wreaked devastation and starvation in Gaza. Selfies of Israeli soldiers preening proudly in bomb-crushed Palestinian neighborhoods. A crackdown on even mild forms of dissent among Israelis.