That's actually not true. The Islamists in Iran arose because Iran's fledgling democracy was destroyed and the Shah reinstalled and propped up by the US. They were in the process of building a democracy in that country, and they had a totalitarian dictatorship imposed on them from the outside. The rise of Islamism in that country was a response to that.

In Afghanistan, the Taliban arose because of the complete destruction of Afghan societal structures and the civil infrastructure because of the US and Soviet Union fighting a proxy war in that country. In the wake of that war, the Taliban arose in answer to the total breakdown of all societal structures and the resulting total chaos there.

al Qaeda seeks to remove Western forces from Muslim countries, and their numbers are increased every time Western military aggression results in destruction and death in Muslim countries. They are a response to outside interference, not the other way around.