Now I am a teacher of the Transcendental Meditation technique. I see people coming to learn who are concerned that TM doesn't interfere with their religion, as well as those who are are looking for a way to access the divine from within. Religious folks commonly find more meaning in their scriptures when they meditate, and the non-religious find their own words to relate to their experience of serenity and union with the divine.
Most likely, the daily practice of transcending the material world and gaining the non-material, purely spiritual side of life was once an important part of all the great religions, but over time understanding became distorted and lost. I think this meditation can re-enliven the great religions and make them more relevant, as well as bring spirituality to those who have no religious beliefs.