I am a religious person, and I am undoubtedly a mystic:
“Mysticism (from the Greek μυστικός, mystikos, an initiate of a mystery religion) is the pursuit of communion with, identity with, or conscious awareness of an ultimate reality, divinity, spiritual truth, or God through direct experience, intuition, instinct or insight. Mysticism usually centers on a practice or practices intended to nurture those experiences or awareness.”
Mystics don’t “believe in” God, we experience God, or “ultimate reality,” or “divinity,” or “spiritual truth” directly. Thus it doesn’t really make sense to ask if I “believe in God” or, when I know that someone is good, how I “know” that they are good. I just do. Can I be wrong? Yes. But my opinion is not based on arguments that can be stated; my opinion is a direct perception of reality, just as you directly perceive whether you like a color, a sound, or a taste.
Thus my emphasis on the importance of intuition as “the still small voice within” or God. And I encourage you to develop your intuition, on the grounds that I believe that once you learn to hear the voice of God clearly on your own, you will be a very powerful mystic, and all your fears and doubts will disappear.
Sufism is the mystic branch of Islam.