They were optimistic!
Looking at the long term history of Israel, the left was more optimistic in general about hopes for peace with the Palestinians, while the right more suspected that Arafat never really wanted peace, and was just being sneaky. But let it be noted that the Prime Minister who ordered the withdrawal from Gaza was right-wing Gen. Ariel Sharon, Likud member and previous advocate of settlements everywhere.
After the actions of Hamas in subsequent years, particularly Oct 7, 2023, that hope and optimism was completely eliminated.