Israel's current rulers tow the line on attacking anything and everything Islamic. This, while they tacitly carry on relations and dirty tricks with numerous Islamic nations, such as Saudi Arabia, Jordan, UAE and so on. By all accounts, the Morsi government was working security issues, trade, and other issues with Israel. Nonetheless, an Islamic nation is an evil nation, in the eyes of Israel, even if they have a peace treaty with it. It is a misconception to believe that a secular nation will be more accepting of Israel than an Islamic one. A secular nation will still remember that Israel invaded Egypt in 1967, and bombed most of it's airforce while it sat peacefully on the ground. And for those revisionists who dream that Egypt started that war, refer to the recent re-enactment, or wickpedia for confirmation. A secular government will still be aware of the multitude of refugees that Israel has created with it's wars, land theft, and criminal court system that retroactively legalizes land theft. When Israel gets right with the neighbors it has in the region, it's problems will diminish, be they Islamic, or secular governments.
Australian Islamic State recruiter killed in U.S. airstrike in Iraq (Reuters)
from the article: Israel urged U.S. not to halt aid to Egypt, says top American official