1. Barring any defeater for the belief that a religious experience is genuine, the person with the religious experience is justified in believing that this experience is true - that this belief possesses verisimilitude (Premise)
2. There are many people who have had religious experiences without any defeater for their belief in their experiences' verisimilitude. (Premise)
3. Therefore, these people are rationally justified in believing in the verisimilitude of their religious experiences. (From 1 and 2)
Notice I've weakened the argument's premises. I'm not talking about these beliefs based on religious experience being rationally compelling, but simply being rationally acceptable. In the absence of insanity or any other defeater, then a person perfectly within his or her epistemic rights in accepting a religious experience as genuine.
Some object that there are conflicting religious experiences, but that poses no problem for at least two reasons. First, many of these "conflicting" religious experiences have more in common than we're often led to believe. Religious experiences are quite often the manifestation of some Supreme Being, whether that's the Biblical God, Allah, Brahman, etc. Secondly, we have to keep in mind the nature of defeaters. Imagine you and I are standing at opposite sides of a garden. You see a white flower, even though my perception of the same flower leads me to believe it is a purple flower. Should I just abandon my belief simply because there is a conflicting experience? Of course not! Now, if it could be shown that there is a light hanging over the garden that, when standing at a certain angle, will cause people to view white flowers as purple, then I would have a defeater for my belief. (Credit goes to William Alston for this reply to the objection.)
I want to mention, however briefly, St. Joan of Arc. She experienced visions, which would rank very highly on the religious experience chart. What's more, historians are almost universally agreed that Joan sincerely believed she was having these visions. This is important because "liars make poor martyrs," as the saying goes. That leaves us with either insanity or that Joan was in fact telling the truth. Unfortunately for Naturalists, every mental disorder has been almost unanimously rejected when it comes to Joan's visions. Other hypotheses have suffered the same fate. Nores and Yakovleff comment, "It is difficult to draw final conclusions, but it would seem unlikely that widespread tuberculosis, a serious disease, was present in this patient [Joan of Arc] whose life-style and activities would surely have been impossible had such a serious disease been present." 
 J.M. Nores and Y. Yakovleff, "A Historical Case of Disseminated Chronic Tuberculosis," Neuropsychobiology 32, 1995, pp. 79-80.