Familists were pacifists, believed that the world was governed by the laws of nature rather than divine intervention, and denied the trinity.
Unsurprisingly, just like modern movements of this nature, Familists were primarily students, scholars, and artists, and the faith was concentrated near the University of Cambridge.
Familists managed to escape execution and persecution by not generally telling anyone outside of the Family about their beliefs, ("The first rule of Family Club is don't talk about Family Club,") and proper respectable members of other, respected churches. They believed it was important to at least act outwardly like everyone else.
Nevertheless, we do know of a few Familists who've come to historical attention, including Phillip II of Spain's printer (he printed Catholic documents by day, and Familist ones by night,) and some of the Yeomen of Elizabeth I's guards.
Familists seem to have disappeared in the early 1700s--their low-key approach to spreading their theology had always made the group's long-term survival unlikely.