As for who the Egyptian government considers too radical, it is easy enough to understand, but hardly fits the monolith our own bigots want to construct ("all Muslims agree with each other, are bad"). I don't quite see why; the reality of the thing is damning enough, if what they are after is rhetorical ammo.
There are something like 30,000 Muslim activists jailed in Egypt without trial, many of them routinely tortured. What marks them as "radicals" to the government is not their strident belief, nor hatred of foreign infidels, but hatred of *the government* as insufficiently Islamic. The government is based on successors of Nasser; its ideology is modernist Arab nationalism, not Islamic fundamentalism.
The Islamic radicals (Muslim Brotherhood types) denounce the government as secularist, unbelieving western lackies, corrupt, cowardly, and traitorous. They want an Islamic revolution to abolish the existing Arab nationalist government and impose Shariah law. That is a radical, in Egypt.
Hating Israel, in contrast, is something the Arab nationalists and the Islamic radicals can agree on. Meanwhile anyone talking mostly about morality or culture or real learning is way over on the enlightenment side. What would correspond to the center *left* in Egypt has political opinions akin to Mussolini's. The issue that defines the spectrum, incidentally, is attitudes toward modernity, not toward the economic system.