Question says mostly all. To be more concrete, I am talking about the popularity of Krishna and Buddhism on the religious side, and stuff like yoga on the more practical side. Some other things might be the popularity of "gurus" etc.
Perhaps one of the most influential things that raised awareness and popularity with these cultures was the involvement of the Beatles in exploring their own "spiritual awareness". At the height of their popularity, they drew a lot of attention to these alternatives to spirituality. The drug culture of the late 1960's included a very large movement of American youth who were looking for alternatives to the staid lifestyles their parents had tried to impose upon them. There were other popular musicians of that period who had similar impacts, as well as a growing number of "gurus" who capitalized on it, but the timing of the Beatle's interest and the rise of the popular drug culture combined to encourage a lot of youth to start exploring other options.
This religio-cultural trend became a very important and influential motif of East-West exchanges from about the last quarter of the nineteenth century onwards - possibly the most important religio-cultural trend, from the Indian point of view, if yoga is understood in its broadest definition. This trend took tangible form in 1896, our second important date, when the Indian reaction to Western missionary efforts took shape in the counter-missionary project of the young and influential Swami Vivekananda. The date marks the publication of his volume on Raja Yoga. The great impression that the Swami made at the 1893 Chicago Parliament of Religions and the subsequent establishment of the Ramakrishna movement are usually referred to as his main achievements.
South Asian religion entered the United States in at least three distinct waves.
The first wave was almost purely literary: In the later half of the eighteenth century, a group of scholar-officials working for the British East India Company translated some of the more important Hindu religious scriptures into English. The ideas contained in these texts directly influenced the transcendentalist movement (evident in such compositions as Emerson's "Over-Soul" essay) and, both directly and indirectly, influenced New Thought. Translated Hindu scriptures also contributed to Theosophy, and the literary presence of Hinduism was at least partially responsible for inspiring Madame Blavatsky and Colonel Olcott's visit to India—a visit that further reinforced the Theo-sophical tendency to draw inspiration from Mother India.
The second wave was set in motion by a handful of Hindu religious teachers who visited the United States in the late nineteenth and early twentieth centuries. While Protap Chunder Mozoomdar was probably the first Hindu to lecture to American audiences/ the reformed Hinduism of the Brahmo Samaj which he represented did not make a lasting impression on the American religious imagination.5 Far more significant in terms of long-term influence was Swami Vivekananda, who visited the United States in 1893 and who was the most popular speaker at the World's Parliament of Religions in Chicago. Vivekananda eventually gathered enough support to establish the Vedanta Society in New York, an organization which, because of its publishing activities, has had an influence out of proportion to its membership. Another important Indian religious teacher to enter the United States during this early period was Swami Paramahansa Yogananda. In addition to the ongoing influence of his organization, the Self-Realization Fellowship, his Autobiography of a Yogi has inspired thousands of Westerners to undertake Eastern spiritual disciplines.
Following the raising of immigration barriers in 1917, Asians were unable to enter the United States in large numbers until after these barriers were lowered in 1965. In the late sixties and early seventies, a new wave of Indian gurus found a receptive audience among young Americans seeking religious inspiration from nontraditional sources. While the spiritual subculture of the seventies was comprised of Buddhists, Sufis, and other non-Hindu groups, Indian spiritual teachers were the most numerous (as well as, in the long run, the most influential). This spiritual subculture, which was in many ways the successor movement to the counterculture of the sixties, led directly to the New Age movement of the eighties.
- Note: the emphasizing is mine and is not found in the books.
This relates to the "discovery" of Asian, and other non-European cultures by Americans.
As of the middle of the 20th century, American society was pretty homogeneous, and "Eurocentric." An expression used is that American culture of about 1950 came in three flavors "chocolate, vanilla, and strawberry," like ice-cream.
We all know what happened to ice-cream tastes; they went from the above three flavors to the 31 of Baskin Robbins. A similar thing happened in the rest of American culture, and Indian and Bhuddist were included in the "31 flavors."
I would say the seed of interest in Indian/Hindu culture was sown when Swami Vivekananda visited America and spoke at the Conference of World Religions. Later a few gurus such as Srila Prabhupada, Paramahamsa Yogananda spread word in America. The rise of interest in the 20th century , of course, is largely due to the Indian immigrant population in America as well as the rise of interest and opportunities to travel the world.
In Hinduism and Buddhism there is message of peace and an encouragement to not be materialistic. Also, spiritualism is a path that leads your spirit to "moksha", or freedom, and there is also the popularity of "yogasanas"and "pranayama" who tend to have strong influences on their followers.