The one overriding comment I would make when looking at yoga past, present, or future is that people should realize that there never was “one” yoga.
Yoga has meant a variety of things to a host of people over the millennia: it can be a practice or the end result of a practice; it can be union or it can be divorce and liberation from a non-dualistic world view; it can be Hindu, Buddhist, Jain, Sufi, Christian, etc. No one invented yoga, no one can claim ownership (including cultural ownership) and no one can determine what yoga should be. Imagine if someone said “only Christians are allowed to pray and only Christians know the proper way to pray!” Prayer does not belong to anyone so anyone can pray, and do so in their own way.
See also The Ancient & Modern Roots of Yoga
Going forward yoga will continue to defy definition and attribution. Is it a physical practice meant to regain or maintain health? Yes, and this dimension of yoga will continue into the foreseeable future. Is it a psychological practice meant to reduce stress and anxiety and promote wholeness? Yes, and this meditative psychotherapeutic practice will continue to develop. Both the physical and psychological aspect of yoga will be informed more and more by modern science and less by the over-the-top claims found in the traditional text (such as “Padmasana is the destroyer of all disease” found in the Hatha Yoga Pradipika) or even the anecdotal evidence of teachers in the 20th century. But yoga is also for many a spiritual practice and this aspect will continue, but I sense not to the same degree as the more secular branches of yoga practices. Even here though, there will continue to be space for these spiritual awakenings to be completely at odds with each other: one person will awaken to a realization of the unity of all beings (non-dualism) while another will awaken to the sense of aloofness from the material world (kaivalya, which is dualistic.)
So, whither yoga? Where it has always gone: different things to different people, and in new unpredictable ways as the future has always unfolded.