In MSMspeak, "Conservative" simply means "Bad Guys." Thus, Ayatollah Khomeini was a "conservative." Now you would think that might make The Shah a "liberal." But no, it doesn't work that way. He was a "conservative" too, because they didn't like. In the same way, Mao and Brezhnev and Stalin were "conservative" Marxists (yes, normal people realize how stupid that is, but not reporters.)
Conservative is not noun, but adjective describing a trait. It is a being traditional, not accepting change(any change, good or bad).
Koran literalists are conservatives. They aren't radicals at all. Calling them radical Islamist is a misnomer. They don't shift from Koran at all.