Jim Stone:  "In short, religions relate practitioners to a reality that
transcends the mundane world revealed by sense perception; we
might call it a 'supermundane reality.' "

I think the last concept has not received the attention it deserves, although it's been adverted to by several: John Mc Creery 2009-10-30; Herbert Huber 2009-11-03; Derek Allen 11-04. Most recently, Ms E. Cameron quoted Kenneth Little,

''in 'The Mende of Sierra Leone' the chapters on religion , and on secret societies. The author, Kenneth Little, a social anthroplogist, explains that what modern educated people call 'supernatural' is not regarded as substantially so different from natural.''

I appreciate that Jim S. was trying for neutrality in avoiding the term 'supernatural,' but 'supermundane' may be equally open to question. On the one hand, as Derek Allen suggested, the love between Romeo and Juliet  may qualify; the term is hopelessly loose. On the other hand, the term 'transcend'  and Jim's statements such as,

"It comprises a level of reality deeper than what sense perception (even assisted by scientific instruments) reveals, and its nature is best discovered by other means, e.g. meditation."

suggest a strict sense: that the world as described by the natural and physical sciences is one which religious persons allegedly go beyond, using special methods to do so. Jim introduces a bifurcation, which, to the believer, does not exist, at least in the way Jim describes it. (Obviously practices connected with what's held sacred are by definition, not routine and 'mundane'.)

Jim S, so far as I can see,  has given no answers to queries on this issue, and I've looked at a portion of the auxiliary paper he posted.

A basic question is, Can there be a neutral definition? Jim S says, indicating his intention along those lines,

"As all such beliefs [in the supermundane] may be false, there may be no reality that transcends the mundane world revealed by sense perception. All religions may be fundamentally mistaken. There is nothing in my account that a complete atheist couldn't accept. "

Derek A made the point well in this example:  "It's like saying that falling in love is "carrying out certain ... conventional courtship practices associated with a belief in the superior qualities of a particular human being."

Again, a certain type of psychological account might be couched in such terms, but at the cost, as DA suggested, of ignoring experience (where truth of belief is assumed). More fundamentally, the well known 'emic' 'etic' issues are raised. Since I am no anthropologist, I'll leave this anthropological debate to McCreery, Cameron, and others.

In philosophical terms, the set up proposed by Jim S. seems almost inevitably to suit the a priori position of the skeptic. Whether the love of Romeo and Juliet strikes Jim S. as 'supermundane,' I don't know. Perhaps not. But, if we take 'supermundane' in a strict sense, the religious person is set up for the classic Ayer-ian retort, "Ah, you're involved in metaphysics," and the next step is what Hume recommended for books dealing neither with mathematics, nor fact.

Jim S's account, despite its merits and lucid defense, seeks neutrality, and thus misses a key feature of most religions (perhaps all; I'm not discussing essence v. 'family resemblance'):  A holistic reality (notwithstanding the existence of 'planes' or subcategories). The statement,

In short, religions relate practitioners to a reality that transcends the mundane world revealed by sense perception; we might call it a 'supermundane reality.' 

is fundamentally inaccurate, if read in the most obvious way, i.e., extensionally (de dicto).  It's like saying, "The Greeks believed that the goddess Aphrodite was connected with the second planet circling the sun."