Pretty much for the same reasons that people believe in the occult and esotericism today. In every generation, the majority of people believe in the supernatural in one form or another (religion, horoscopes & astrology, homeopathic medicine, ghosts, etc.), and for a subset the interest runs deep enough that they become attracted to groups or studies outside of the cultural norms.

In the 19th/20th century United States of America in particular, there was a substantial cultural shift and uprising in spirituality known as the Third Great Awakening, which overlapped or coincided with similar rising interests in occultism, Spiritualism, neo-Paganism, and psychic research. The reasons are diverse: the stress of major wars like the American Civil War and World War I likely facilitated some interest, as did the increasing availability of occult or esoteric material through mass printing and scholarship, and, somewhat ironically, scientific discoveries which undercut the theological dogma of some established religions.

It was all of these things, and yet more than all of that. The New Thought Movement (1830s), the Theosophical Society (founded 1875), Marie Baker Eddy's Christian Science (founded 1879), the Hermetic Order of the Golden Dawn (founded 1887), the Moorish Science Temple of America (founded 1913), all combined aspects of "science" and existing religions, claiming to reveal either new or ancient truths. There were fads, borrowings, and not a few would-be prophets and occultists that were indisputably hucksters - but there was, at the same time, some people for whom existing religious doctrines did not meet their spiritual needs.

Owen Davies in his introduction to The Supernatural War, looking at superstition and occultism in the popular consciousness with regards to World War I, notes:

Violent collective crises generate many extraordinary personal and national experiences that transcend both our sense of reason and our understanding of the boundaries of the possible. [...] Supernatural visions, such as the notorious appearances of ghostly medieval archers at the Battle of Mons in 1914, were reported and debated in a way never before experienced in national public life. Churches, occultists, and psychical researchers across the warring countries saw opportunities to extend their horizons and influence, while the public reached for traditional and novel ways of coping with the realities of warfare.

There were other reasons. The Moorish Science Temple of America, for example, emphasized the racial injustice endemic in the United States of America during the period. Spiritualists were often also abolitionists and supported women's suffrage. Christian Science and Theosophy were much more open to women in leadership roles, providing greater opportunities for women to advance.

Yet the individual reasons are going to be unique, dependent on personal circumstances and proclivities. Most of the focus on these individual movements and churches tend to focus on the leaders and founders rather than the rank-and-file - but there are plenty of people who find themselves having experiences they could not explain but which jived with some strange experiences of others, or were drawn seeking answers beyond those offered by existing religions. Some of these were caused by moments of crisis - a tight spot during a battle, a mother at home lamenting the death of a son or husband, several economic hardship and migration - and some just were just convinced by a particularly charismatic preacher.

Keep in mind, most of these groups and movements weren't the robe-and-wavy-daggers sacrificing the virgin on the altar types (even the Church of Satan, founded in 1966, wasn't advocating or practicing actual murder). There were always a few extreme examples that went all-in on the funny robes and things, but most of them were just normal people that were struggling through ordinary lives, with all their quiet problems and desperations. Intelligent people that were willing to keep an open mind - and some wandered in and left, and some stayed.