Zinn is founder of Mindfulness.
Nat Hahn is Buddhist Zen Master. Nyanaponika is a Theravada monk

Everyone wants everyone to do mindfulness. They say it's not Buddhist and it's not pantheistic. But it's both.... here is why. 

Dr Jon Kabat-Zinn ( JKB ) is attributed as the developer/founder of Mindfulness. JKB not only practiced but taught Hatha Yoga and studied meditation with renown Buddhist and Zen Buddhist masters. Both Yoga and Buddhist meditators experience “ Samadhi” which they “arrive at by inference” as the sensing of their “ I-Am-Ness” when one is in a moment the Highest, Lord of Reality and also the lowest of beings. The names for this peak experience are – Universal Consciousness, God Consciousness, Nirvana, Liberation, Sartori, Advaita, Non Dual, etc which science attributes to a combination of neural phenomena Click: S #01- 07.

These neural phenomena drives the experience where one is unitively ONE with the UNIVERSE which is the very basis of pantheism, a doctrine which identifies God with the universe, or regards the universe as a manifestation of God M #07 

Since Mindfulness use the same meditative practices as that of Yoga and Buddhism, the same neural phenomena occur and the sensing, experience and inference of these neural phenomena which had historically given rise to pantheistic mental concepts which formed the very basis of their spiritualistic worldview are now felt by those who practice Mindfulness. M #07 

You may argue that these neural phenomena may be re-interpreted and set within science and therapeutical frameworks,….. but over thousands of years, over diverse cultures and opposing religions, the interpretation of these neural phenomena are identical and  pantheistic.M #07

External Links :

#1

The current wave of mindfulness therapies, mindfulness coaching, mindfulness exercises, etc., owe most (or perhaps everything) to a stress-reduction program developed in the late 1970s by Dr. Jon Kabat-Zinn, a professor of medicine emeritus at the University of Massachusetts. https://welldoing.org/article/basics-of-mindfulness-come-from

#2

Mindful Yoga by Jon Kabat-Zinn ( Hence in Zinn’s own words …. )

For a number of years in the late 1970s, Larry Rosenberg and I taught back-to-back evening classes in a church in Harvard Square. He would teach vipassana meditation (a Buddhist practice of mindfulness), and I followed with mindful hatha yoga.

http://www.makingsenseofmentalhealth.org/articles/mindfulyoga.pdf

 #3

Kabat-Zinn was a student of Buddhist teachers such as Thich Nhat Hanh and Zen Master Seung Sahn and a founding member of Cambridge Zen Center. His practice of yoga and studies with Buddhist teachers led him to integrate their teachings with those of science. https://en.wikipedia.org/wiki/Jon_Kabat-Zinn

Quote from Thich Nhat Hanh – “ The image of Jesus presented to us is usually of Jesus on the cross. This is a very painful image for me. It does not convey joy, or peace and this does not do justice to Jesus. I hope that our Christian friends will also portray Jesus in other ways, like sitting in the lotus position, or doing walking meditation. Doing so will allow us to feel peace and joy penetrating into our hearts when we contemplate Jesus. This is my suggestion. “

#4

Samādhi (Sanskrit: समाधि, Hindi pronunciation: [səˈmaːd̪ʱi]), also called samāpatti, in Hinduism, Buddhism, Jainism, Sikhism and yogic schools refers to a state of meditative consciousness. It is a meditative absorption or trance, attained by the practice of dhyāna.[1] In samādhi the mind becomes still. It is a state of being totally aware of the present moment; a one-pointedness of mind.[web 1]

https://en.wikipedia.org/wiki/Samadhi

#5 ( an example of the Samadhi experience )

When one has this sahaja samadhi, one becomes the Lord and Master of Reality. One can go at his sweet will to the Highest and then come down to the earth-consciousness to manifest. http://www.srichinmoy.org/spirituality/concentration_meditation_contemplation/samadhi

#6 ( a deconstruction of Samadhi )

Savichara, "reflective":[43] the citta is concentrated upon a subtle object of meditation,[web 8][43] which is not percpetible to the senses, but arrived at through inference,[43] such as the senses, the process of cognition, the mind, the I-am-ness,[note 17] the chakras, the inner-breath (prana), the nadis, the intellect (buddhi).[43] The stilling of reflection is called nirvichara samapatti.[43][note 18]

Sananda Samadhi, ananda,[note 19] "bliss": this state emphasizes the still subtler state of bliss in meditation;[web 8]

Sasmita: the citta is concentrated upon the sense or feeling of "I-am-ness".[web 8]

https://en.wikipedia.org/wiki/Samadhi