Can you please explain how Hogwarts in Harry Potter and the Sorcerer's Stone compares to secret societies devoted to alchemy and hermetic pursuits, such as the Rosicrucians?

The Rosicrucians claimed to have access to mysterious, hidden knowledge from the ancient past, which could provide spiritual and intellectual enlightenment. Their ideas came from places like the Kabbalah or Jewish mysticism, mystical Christianity, and alchemy—the latter of which has the ultimate end goal of creating the philosopher's stone, a famed item that can turn metals to gold and provide immortality.
In Harry Potter and the Sorcerer's Stone, or, as it is titled in the U.K., Harry Potter and the Philosopher's Stone, Harry is introduced to a world of mysterious, hidden, ancient knowledge. Hidden away from ordinary people, Hogwarts is a place where specially selected people with special knowledge and abilities meet to gain an education in magic; they have been doing this in secret for a long, long time, since the school was founded by four founders in 990 C.E. When considering this in the framework of secret societies dedicated to esoteric and hermetic pursuits, it's possible to find a lot of similarities—like societies like the Rosicrucians (or at least like those societies claimed they did), Harry and his magical community are secretly gaining ancient knowledge in order to achieve a certain type of enlightenment.
More literally, one of the things Harry is seeking at Hogwarts is the sorcerer's or philosopher's stone. In Harry's case, it is not about making the stone or trying to find it for personal gain—the stone has already been made, and he is desperate to protect it from Lord Voldemort. But in order to achieve his goal and find the stone to protect it, he, Ron, and Hermione research with many old books in the Hogwarts library (a secret to the greater world, filled with ancient and modern magical texts) and learn advanced magic in order to go through the obstacles leading them to the stone. In addition to Hogwarts being a secret and exclusive place itself, Harry and his friends are searching for the stone in secret from everyone else, creating their own little society of private adventures and knowledge.
Like those secret societies dedicated to ancient esoteric knowledge and the pursuit of the philosopher's stone, Harry and his friends use ancient magical knowledge to find what they are seeking in secret—not only because they are attending a secret magical institution that has existed for thousands of years, but also because they are keeping their quest a secret from everyone around them.