his collection of religious experiences does seem to have been dominated by various Protestant incarnations. There is so much internal variety that I think James thought he was covering the field.
I also think James would argue that he was writing about the breadth of religious experience, and that this is primarily determined by human nature and personality rather than the religion itself. Both 'the sick soul' and the 'healthy minded' believer have representatives in every experience.
I think one thing that makes people uncomfortable nowdays is James's inclusion of nonreligious belief systems along with various faiths. For example, in the chapter on conversion, he prominently includes a conversion to atheism.
Maybe it's my psych major background, but it makes sense to me to look at how human belief systems function across faiths and non-faiths in the way that James did. It's certainly not the only way, but it helps distinguish what is human from what is part of the belief system itself. This is part of what is frustrating about the new atheists is their complete cluenessness that any traits or patterns common to adherents of a belief system apply to them despite how obvious it might be to anyone else. It is a syndrome common to everyone, but especially the young.
James's writings were groundbreaking a century ago. They are fascinating partly because they are such vivid period pieces, but they are also outdated. Belief sytems are universal. I wish there had been more development of James's basic approach by other people in the last hundred years.