As Aaron has stated, the definition of mysticism is skewed in the West. I would put much of the blame upon the early Roman Catholic Church, since discrediting all other forms of belief was vital to the success of the new government-sponsored religion.
I am a member of AMORC (Ancient Mystical Order of the Rose Cross) better known as the Rosicrucians, but I still consider myself a Deist. This is a form of mysticism that is compatible with almost any religious belief one might hold, and we have members who continue to be active in their churches. I found that fact troubling at first - how can one become enlightened and still believe in one's old religion? - but I have been told by other members that the knowledge gained from Rosicrucian teachings allows them to interpret their church's teachings in a way not usually expressed by their ministers.
The principles of Rosicrucian mysticism is based upon the teachings of the ancient Egyptian mystery schools - "mystery" meaning that these precepts were only passed on to select students. The masses have always had their watered-down religious teachings, while a select few studied on a deeper level (think about monks, for example).
Everything presented in our teachings is accompanied by a practical experiment. No one is expected to accept anything they can't prove for themselves. I'd call that rational mysticism, wouldn't you?