I suppose we're starting from a 'logical' position - asking what 'reality' means in this context - of course Middle earth is not 'real' in the sense of having actually existed in the primary world, so its reality
must be a secondary reality. In the primary world it cannot be real, so its 'reality' must come down in the end to self consistency. It is fully imagined - even to the extent of including people, places & things which play no part in the main story. It is 'real' within its own dimension, which simply means that it is believable to us when we enter into it, enough that we don't question it. So perhaps that's it - its self consistent enough that we don't ask questions & break the spell - or at least that any questions we ask about it can be answered - it contains sufficient 'redundancy'.
But if we are to accept it - & which is more important, if we are to feel it to be relevant to us, then we must be able to relate the people & events of the story to our own 'primary' world. So, its 'reality' depends not only on its internal self consistency but on its relevance to our world. Its not 'real' to us simply because it is a self contained, logically consistent , world, but because we can relate it to our lives. So, 'reality' depends on applicability - but not on any 'allegorical' aspect it may contain (yet where do the two meet?:
http://www.geocities.com/ct70815/my_page.html). Clearly, it isn't simply a matter of relevance alone, though, as an allegory may seem 'relevant' & yet not 'real'.
What I'm trying to say (sorry, but I'm still in shock after reading the article on the above link - thanks (?) to TORN for that, btw!), is that there are two kinds of 'reality' involved here - one is the 'reality', ie the conviction that the secondary world carries that it is 'true' & the other is the 'reality', ie the relevance it has for us in our lives.
For me, Middle earth is 'real' in both ways, & its that that speaks to me so strongly.
If none of that makes sense you'll have to blame that Carole person!