I think they will continue to grow for the foreseeable future. Or, at least, new-agey, westernized bits and pieces of eastern religions, as these elements tend to appeal to a growing contingent of the population who like to pick and choose various esoteric, feel-good beliefs and superstitions.
Actually, that started a few hundred years ago (or longer). For example: "The notion of Hinduism is itself a Western-inspired abstraction, which until the nineteenth century bore little or no resemblance to the diversity of Indian religious belief and practice." (from King, R. (1999).
Orientalism and Religion: Post-Colonial Theory, India and" The Mystic East". Routledge). King quotes part an interesting recording of a conversation between Thierry G. Verhelst (who was a member of the PhD working group behind the volumes Religions and Cultures) and "an Indian intellectual from Tamil Nadu". The question was "Are you a Hindu?".
The answer was "No, I grew critical of it because of casteism ... Actually, you should not ask people if they are Hindu. This does not mean much. If you ask them what their religion is, they will say, I belong to this caste."
King is hardly alone, being neither the first nor certainly the last to argue that "Hinduism" began as a Western categorization and (for those who disagree that it was a Western construction) became a politically and socio-culturally based synthesis in opposition to colonialism. So on the one hand there are those like B. K. Pennington whose 2005
Was Hinduism Invented? Britons, Indians, and the Colonial Construction of Religion (Oxford University Press) is arguing exactly that (that it was an invention or construction of colonial dynamics), and numerous others who see varying degrees of continuity, authenticity through nationhood and constructed self-identity, etc.
The extreme constructionalist versions seem to me to be obviously problematic, as we actually have texts written long before Europeans began to travel into the places like India, China, etc. But I don't think anybody (at least among historians, philosophers of religion, etc.) would argue that European conceptions were grafted onto Eastern practices and beliefs.
They may face opposition from traditional, western religions, but I doubt they will have much influence in how much eastern religious concepts spread.
They already have. As a concept, "religion" itself is (or is at least partly) a Western model into which the beliefs, practices, and traditions of other cultures have been forced. Two particularly influential works here are Dubuisson's
L'Occident et la religion: Mythes, science et idéologie & Masuzawa
The Invention of World Religions: Or, How European Universalism Was Preserved in the Language of Pluralism.
I'd say they have a greater affinity with spiritual, new-agey, and mystical movements
The term "mysticism" has similar problems. The modern use of the term comes from Christian polemic discouse of the 1500's, and (as far as I know) was first applied to the practices and beliefs of the "Orient" by Cowper in 1781. However, in "
The Making of Modern Mysticism" Schmidt states: "Through the early decades of the eighteenth century, the English category of mysticism did not exist. The prevailing classification instead was mystical theology, and it signified a specific devotional branch within Christian divinity." Moreover, while the term was used almost entirely as a derogatory one, it seems that when applied to "the Orient" and Eastern "mysticism" it was more nuanced, sort of like the myth of the "noble savage": a romanticized ideal which somehow both positive and yet only via its relationship to the idealization of "primitive" folk which was a popular theme of the day.
Historically, the idea of "religion" as the belief in things like gods, animism, creation cosmologies, myths, etc., was one of practice, while ethics and morality were communal and based on social norms rather than religious beliefs, while philosophy (where it existed) was a seperate discipline altogether.