Interesting argument, I'm afraid. The problem certainly seems to be Islam.
There is one minor--or maybe not so minor--point that I'd question in this article, and in fact it only makes his argument more persuasive. The author translates "Darul Islam" as "house of peace." I wonder if "house of submission" isn't more accurate.
There's the nub of it. Islam demands submission to the absolute decrees an arbitrary God and submission to arbitrary rulers who claim authority in Allah's name. There is no such thing as free will, and therefore no possibility of political freedom.
Yes, fundementally incompatible I'm afraid. There are lots of people who are extremely uncomfortable thinking for themselves, and welcome a strict structure imposed on their lives. It certainly makes life easier.