Reddit mentions of The Secret Doctrines of the Rosicrucians (Ancient Mysteries Series): Revelations about the Ancient Secret Society Devoted to the Study of Occult Doctrines, ... and the Manifestation of Occult Powers

There were definitely historical occult activities and secret orders involved throughout the medieval and renaissance periods in Europe and we know of a few Knights involved with them. What you are looking for is not within the scope of HEMA as this moniker relates only to the "martial arts" of European history. However, there are some I am certain that are still involved in the martial arts of HEMA and also still engaged in fraternal orders and mystical contemplation. No doubt you will discover modern fencers who are also adepts of some order such as Rosicrucianism. You can find some basic info about this order here: https://www.amazon.com/Secret-Doctrines-Rosicrucians-Ancient-Mysteries-ebook/dp/B01B1JGKUW/ref=pd_sim_351_35?_encoding=UTF8&pd_rd_i=B01B1JGKUW&pd_rd_r=9da93dff-bff3-4796-b714-17cd93f896ff&pd_rd_w=CLoqa&pd_rd_wg=WsCE6&pf_rd_p=5abf8658-0b5f-405c-b880-a6d1b558d4ea&pf_rd_r=6XMHK2AQXK7NH91X70PN&psc=1&refRID=6XMHK2AQXK7NH91X70PN

It is also worthy to note that there are those involved in orders such as the Knights of Pythias. Case in point, one HEMA'ist who wrote a book on the modern application of Chivalry as a guide for inspired living can be found here: https://www.amazon.com/Knightly-Virtue-Living-Modern-World-ebook/dp/B07VN9DXM4/ref=sr_1_1?keywords=knightly+living&qid=1573049374&s=digital-text&sr=1-1

Hope this helps you on your search.