I think the mistake and the fear that many GOP people harbor is that they think Obama is like their own ilk. Most people judge others based on their own narrow "filter" that they view the world from. In other words, a republican would fear that Obama's associations would determine who he is. That is because republicans are very much herd-thinkers. They follow their leaders without question...that's why they have been so successful in past elections; whereas as you know, the democrats splinter and fractillate due to differing opinions.
Now tell me who the free people really are, the true patriots?
So republicans fear that because Obama has had contact with various different mindsets, that he will adhere strongly to them. Free-thinkers don't weigh their anchor down that much. Obama is no more a stalwart muslim than I am a stalwart party-girl that I was in college. He glanced at it and then glanced at christianity. He's glanced at many things and fixates on few if any.
The republican spin-doctors had quite a party pointing out that he waffles. And yet now they want us to buy that he is a rigidly devoted muslim terrorist. Which is it?