There is only one organized political party in Egypt, that is the Muslim Brotherhood. The MB has been around a long time, and they are the ones who extended the original franchise to al-Qaeda, as their “shock troops”.
The Muslim Brotherhood is just an Arabic version of the National Socialist German Workers Party, and they draw a great deal of inspiration from “Mein Kampf”, which has been translated to Arabic and widely distributed.
People make the mistake of believing the Nazis were some kind of “right-wing” organization, and that is one of the great myths of the 20th Century. There was NOTHING that even remotely resembled “right-wing” in the philosophy or practices of the Nazi party that dominated the Third Reich. That was a piece of disinformation propagated by Stalin, and perhaps only from the perspective of International Socialism could National Socialism be considered to be to their “right” - but still WAY sort of approaching anything like “the middle”.
We may be sure of one thing, the gay faction under the Muslim Brotherhood is not a prominent player in the current series of events in Egypt.
Not disagreeing but would suggest that the appellation "Right Wing" to a totalitarian statist overtly Socialist by name party of pagan homosexual rabble can be better laid at the feet of the American news media and the Democratic party from 1941 (American Communists had a surprisingly positive view of Hitler and his war on the Capitalist democracies until the moment he invaded the Soviet Union) to the present day.