Mindfulness meditation existed way before Carl Jung. It's a basic meditation practice of Buddhism. To the OP, you really don't have to worry about being forced into belief in some sort of god because Buddhism is nontheistic. The basic meditation practices are meant to be beneficial to anyone of any belief system and atheists. I am a Buddhist and an atheist. The Dalai describes himself as an atheist.

There is one lineage (or school) of Buddhism that is specifically meant to bring the practices to anyone and to take out religious/theistic stuff, Shambhala. They have good instruction on mindfulness (sometimes called Calm Abiding or One-Pointed Meditation).