I've seen several Forum pages and arguements discussing why Assassins supported Communists and why not Democracy. I've come up with an answer, feel free to dicuss it down below.
We know that the Assassins support the people not any political institution. Back then the people wanted Communism so the Assassin's supported Communism. They might not have known that it would turn so bad, or they migh have known but wanted people to learn from their mistakes. If they had started a Democracy in place of Communism, chances are that the people would revolt again. S they just followed the People's Will. How about this theory?