Phillip Quinn outlines the basic idea of epistemic parity in the following passage:
The notion of epistemic parity appears attractive from the outset.
Every ethics should include fairness, and epistemic parity seems to
do no more than introduce considerations of fairness into the ethics
of belief. Initially the idea seems simple enough. One should demand
no more, and no less, by way of justification for beliefs in one area
of inquiry than one does in another. Equally stringent standards of
rationality should apply in all cognitive domains. For example, belief
in God should not have to satisfy higher standards in order to be
rational or justified than does belief in the external world or other
minds. (P.L. Quinn, 'Epistemic Parity and Religious Argument',
Philosophical Perspectives, Vol. 5, Philosophy of Religion (1991), p.317.
If this conveys the central idea, one wonders how reasonable it is. Aristotle says in Nicomachean Ethics, I.3, that 'Our discussion will be adequate if it has as much clearness as the subject-matter admits of; for precision is not to be sought for alike in all discussions, any more than in all the products of the crafts' (Barnes, 'The Complete Works of Aristotle', Princeton : Princeton University Press, 1984, 2, p.1730.)
Aristotle clearly recognises that one cannot reasonably expect or require the same rigorous standard of proof from an orator as one can from a mathematician. Equally he himself cannot offer the same degree of rigour in discussing ethical topics as he uses in setting out his logical theory : the subject-matter does not allow it.
Precision and rigour have to be relativised, indexed, to subject-matter. If this is so then the requirement of epistemic parity does not appear reasonable.
But you mainly wanted to know what epistemic parity is. This I hope I have indicated clearly.
As to your rider, if the pluralist endorses epistemic parity in the particular field of religion, and not across the piece, then s/he should apply the same standards of proof or argument to one faith as to another. This need not mean that the two faiths will score equally by the relevant standards, since one may have epistemic merits that that the other lacks : mertis e.g. of consistency, comprehensiveness, clarity, economy of assumptions, &c.