What is the logic behind the Islamic point of view that followers of other religions, and in short the Kuffar (unbelievers) are impure.
In the world, we think about things differently than Allah.
Just consider, we say about a person that he is a rich man because he has money, popularity and reputation but in-front of Allah, the man which has good intentions for everybody, has done good deeds, sincerity is the rich and can buy Heaven.
The best example is,
When a believer utters a lie without a valid excuse, he is cursed by seventy thousand angels. Such a stench emanates from his heart that it reaches the sky and because of this single lie Allah writes for him a sin equivalent to that of committing seventy fornications. Such fornications that the least of which is fornication with ones mother.source
This says that sin is like stench and stench comes from impure things.
We Muslim can ask for forgiveness from Allah and when Allah will forgive, we will be pure but a non-Muslim won't ask for forgiveness and this is what makes them impure.
everything is part of one big harmony. believing is accepting this & "surrendering" to be a part of it. if you don't, you're away from this path. taking sideways. don't know about "impurity", but it's rough on you for one-- on your emotional/spiritual being. whether you're Islamic or not-- although, in my opinion, this is a basic notion of Islam.
not a scholar or anything. just my personal thoughts.