Well, the answer can be easily determined by making some simple observations.
First of all, we are not all Alims here so it would be well advised to consult one on the issue as he might have an answer on this matter.
So what observations can we make?
It is a common practice among those who are in the business of spreading Islam's message i.e. the tabligh to present the Quran as a gift to the non-muslims. The purpose obviously is to make them read the book that they might find some guidance in it.
Now those people who are doing tabligh could not be un-aware of the teachings of Islam other wise what would they be preaching? So such a practice by such learned people shows clearly that is is actually a good practice to not only encourage but facilitate non-muslims reading the Quran. So our first observation can be that if it was not allowed for non-muslims to touch the Quran it wouldn't be being presented to them as a standard practice by the people whose job is Dawah.
It would be interesting to mention that even Saudi Arabia officially does this by organizing events where non-muslims can be made aware of ISlamic teaching and presenting the Quran as a gift.
Now this is an answer from an observation without knowing (or needing to) the theological justification for it.
But still, it might be interesting to know what even a theological analysis offers.
First of all Faisal, the reason why we muslims are asked to do Wuzzu before touching Quran is to my best knowledge based on the Aayah of the Quran mentioned by pakistaniAbroad above as:,
**
[56:79] None shall touch it yamussuhu save the purified ones mutaHarun.**
But it is interesting to note that there is a difference of opinion among ulema as to actually what "mutaharun" i.e. "purified ones" mean.
And this is in the specific refference to what applies in regard to touching the Quran. And still assumes that the Aayah applies to humans and means a physical state and not a spiritual one.
But What physical state exactly?
Some say it is the sate of wuzzu. This is the view subscribed to by the schools where majoirty of subcontinent Ulema seek their guidance from.
That might be why you were taguth to do Wuzzu from childhood. :)
But the other school of thought says (the one prevalent among arabs)
is that this state simply referes to 'Ghusal' and not to Wuzzu.
And this would be a very valid opinion as we know that in the chapter of cleanliness in Islam Ghusal and Wuzzu are seperate states and the Ghusal being known as 'bigger taharat' and Wuzzu as 'small taharat'.
And we also know that actions that break Wuzzu do not break Ghusal.
So "Mutaharrun" need not apply to wuzzu but could be taken as the state of ghussal.
Looking form this point of view non-muslims need not even be required to do wuzzu , nor even muslims, unless they do it anyway as a show of respect. To reinforce this point, it might be interesting for you to know that Arabs don't always make wuzzu before reading the Quran.
This would simplify the problem a lot as the state of ghussal does not have much demands.
If this doesnot clarify the issue or if anyone subscribes however to the view that all non-muslims are 'najas' which is one view than I would refer you back to the first part of this post.
Hope this helps.
This was store policy. If a nonMuslim is discouraged in this manner to browse through a Quran at a store, then i am not certain how s/he is supposed to feel a healthy attraction towards learning about Islam.