Personally I converted from CofE, my parents were disappointed because they thought (rightly) that jws were a cult, but they continued to support me and my jw husband emotionally for over 20 years. My husband converted from Catholicism, again his family were confused, disappointed, but they continue to love, support and communicate with him to this day.
My parents were ranting one day about not speaking to someone who they consider apostate (this person is, but was smart enough to fade years ago). I reminded them both that, by definition, they were apostates from Catholicism, having written formal letters of disassociation. I then asked them how they would feel if both of their families had completely cut them off, refusing to even speak with them. It was comical to see them make excuse after excuse that "it was different because we have 'the Truth'".