Israel trusts Egypt, Morsi or not, enough to settle the cease-fire with Gaza by working through Egyptian military intelligence intermediaries. Israel trusts Egypt enough to authorize the deployment of tanks and other heavy weapons into the Sinai last year to combat arms smugglers.
Egypt has been a US ally for 30 years. We have been supplying military aid for that entire time, but a large part of Egyptian hardware is still of 1970s Soviet vintage. Even with the new addition of M1A1 tanks, Egypt will only have 1000 of them. The other 3000 tanks are vintage pieces which would not stand up to modern warfare. Egypt is not a military threat to Israel.
Morsi’s power grab is of concern. But even if he were to refuse to relinquish power, I am not sure he would be worse than Mubarak, who the US tolerated for many years. Morsi’s leadership role in the Muslim Brotherhood is also of concern. However, he has a country to run and that brings responsibilities that a mere activist does not have.
I would be careful about taking that blog post you cited too seriously. The author is a political activist and the slant in his article is obvious. For example, he makes a big deal of M1A1 tanks, but the US switched to M1A2 tanks 15 years ago. No wonder the US Marine Corps has so few of the older model!