There have already been many spiritual leaders within Roman Catholicism, such as Fr. Bede Griffiths in India, who have spoken of the "complementarity" of religions and advocated a perhaps sophisticated form of religious syncretism.
Perhaps this is a topic for another thread, but I don't know how fair it is to lump people like Griffiths together with Trappists in Kentucky interested in Buddhism. For all the syncretist and even heretical excesses to which Catholics are prone in their attempts at inculturation in India, I believe their starting point is basically a good one--it's basically how St Paul approached the Athenians. They're not doing it like St Paul, to be sure: they could look to the Orthodox Church for clues on how better to inculturate (heck, they could've simply not destroyed us back in the 1600's and they would've seen 1500 years' worth of inculturation in practice), but the basic idea is not a bad one.
That's different from Western monastics in the West exploring non-Christian Eastern monastic traditions from the outside because it's "hip" and Latin's boring.
Yes, I would lump Dom Bede Griffiths in India with Trappists in Kentucky interested in Buddhism. It is true that Fr. Bede initially went to India with the belief in Christ as the fulfillment of all religions, much in the same way as Fr. Damascene and Fr. Seraphim of Platina have written (i.e. Fr. Damascene’s “Christ the Eternal Tao”). He was not properly prepared spiritually to encounter the non-Christian East with its own mystical traditions and various phenomena. The result is that he began to see something deeper and more “spiritual” in Eastern non-Christian experience than what he had experienced from his own spiritually barren monastic formation as a Roman Catholic Benedictine. Being formed under scholastic theology with imaginative prayer (i.e. Ignatian Exercises), having no exposure to or understanding of the patristic hesychastic tradition of Orthodoxy, he saw the drastic contrast between his rational and cerebral approach to prayer and the more contemplative experience of Hinduism. Feeling somewhat betrayed by the poverty of his own formation, he tried to create a Hindu-Christian synthesis, adopting as much Hindu mysticism as he could while maintaining at least formal allegiance to a Christianity of his own making. This left him with a Christian theology which was subservient to the Hindu experience and essentially antithetical to the hesychastic tradition of Orthodoxy.
Similarly, since you mentioned Kentucky, the Trappist monk Thomas Merton became increasingly dissatisfied with the spiritually arid formation he had received and began looking to the non-Christian East to fill the void. He associated his Roman Catholicism with “Christianity”, and not finding fulfillment there, looked outside of Christianity for that fulfillment. This led him to a growing interest in Zen Buddhism and eventually he went to Tibet seeking tantric initiation by a Buddhist Lama, after which he died a rather frightful and untimely death.
Fr. Thomas Keating, another Trappist, when abbot of St. Joseph’s Abbey in Massachusetts invited a Zen Buddhist to teach zazen meditation to his monks. This was not because of some fad, but because of the spiritual aridity of Roman Catholic monastic tradition and the same dissatisfaction experienced by Bede Griffiths and Thomas Merton before him.
Like Bede Griffiths, the Jesuit missionary priest Robert Kennedy and many other Catholic religious have gone to Japan, perhaps with good intentions initially. Yet, like others, they did not have the spiritual formation to understand what appeared to be the “spiritual” depth of Zen Buddhism. The consequence is that, while retaining formal ties to Roman Catholicism, many like Robert E. Kennedy have also become Zen Roshis and their teachings are mostly Zen with Christian terms thrown in here and there, or Christian terms with a worldview that renders Christian dogma and theology subservient to the experience of zazen.
You also have those like Dom Bede Griffiths who started off as an Augustinian, left the religious order, met a Swami, learned mantra meditation with the Swami, became a Benedictine monk, and later began to spread the Swami’s teaching on meditation using Christian terminology as “Christian meditation”. Again, this is not out of a fad, but because he experienced something “deeper” with the Swami than what he knew in his Roman Catholic religious experience. Similarly, his teaching on “Christian Meditation” is essentially Hindu in worldview and in experience of God (mistaking one’s own created spirit of the Uncreated God), yet clothed in Christian terminology that is made subservient to the mantra meditation experience of Hinduism.
Of course, many similar examples could be provided, but what we are speaking of is not the intention of these people, but rather the spiritual ramification of the Great Schism, which itself is the result of Papism (belief in the centrality of the Pope above theological/dogmatic continuity and unity). With Papism came the Great Schism, and with both came the separation of the West from the patristic and hesychastic experience. Roman Catholic religious, associating their Roman Catholic formations with “Christianity”, have not had the spiritual preparation or phronema (patristic worldview) to understand and encounter the mysticism of the non-Christian East. As a consequence, upon encountering the non-Christian East, many sense the poverty of their own tradition and begin to open up to the “spiritual treasures” of non-Christian mysticism. In doing so, they open themselves up to spiritual delusion, dogmatic relativism, and syncretism. These movements attempt to leave behind dogma, which is associated with scholastic rationalism, and emphasize instead the Hindu “experience of the Absolute”, which is not the experience of the Uncreated God but rather the contemplation of the apparent boundlessness of one’s own created spirit. As Elder Sophrony of Essex says, mistaking this experience of one’s own created spirit for the Uncreated God is a greater obstacle to knowing the true God than the grossest passions. One ends up contemplating their own created spiritual beauty and falling into delusion, following the path of Lucifer.
The mystical traditions of all non-Christian religions share this similar experience of the created human spirit, but only in Orthodoxy has been preserved the experience of the Uncreated Energies of God and the hesychastic method. The various religions, exalting this experience of the Absolute above dogma and theology, will easily unite into a universal religion along with the Christians whose Christianity has become subservient to non-Christian mystical experience. Only in the patristic and hesychastic tradition of Orthodoxy is there the sober understanding of true and false spiritual experience and the difference between true and demonic spirituality. The place of the Pope in Roman Catholicism provides the structural foundation for the Antichrist, allegiance to a single head over dogmatic continuity and dogmatic unity; and the spiritual aridity and increasing syncretism found in contemporary Roman Catholicism provides the spiritual foundation for a syncretistic universal religion of the Antichrist which would absolutize some kind of spiritual experience that is accessible to all over adherence to dogmatic teaching.