To suggest that being "Islamic" is tantamount to being an Al Qaeda sympathizer is an uneducated, stupid opinion. Once someone makes that leap, I can't really respect their critique of US policy.
I assume you are attacking people who use the term "Islamic" in its real content and compare all Muslims with Al Qaida. If that is the case, then I agree 100% with you. Unless you meant Islamic as "Islamist", in which case, yes, they very well could sympathize with the theology and values behind Al Qaida, if not the group itself.
I think there's more middle ground than you suggest. Almost every country in the Middle East has a degree fusion of politics and religion. There is a sliding scale between being the Taliban and being a secular regime. There is also a range of aggressiveness towards the United States. Saudi Arabia is an Islamist government that is friendly towards the US. It's a complicated picture.
I personally hate "Islamist" ideology. I hope it is extinguished from the earth. That said, if a country decides to have an Islamist government, but respects their neighbors and international law, I don't see a pressing US interest.