Well, my parents (+rip) belonged to the Church before and after the Council, keeping the faith they always knew, they never went with the new religion and never went sede.
Because although they did not know what happened to their Church (like many other faithful), the knew what was happening within the Church was wrong so they never went along with it. Like many others, they automatically or perhaps better said, inherently or intrinsically stuck with what they knew was right. Reference here the good analogy Last Tradhican gave us:
"U.S. Treasury agents who specialize in forgery detection, when they are being trained, are never shown any forgeries, they are strictly immersed in learning every minute detail of the real thing. That way, they can spot the forgery instantly..."