The SSPX is a "Fraternity" as was made clear to us when I was a seminarian back in mid 90's. Because it is a fraternity the SSPX authorities have no binding authority to command its priests to "follow orders." It is not a religious order such as the Dominicans or Franciscans who order its members to go here or there. There is certainly no authority to bind the faithful, as the "Fraternal Society" does not include them anyway. Bp. Williamson was booted out, and it was not even over doctrine. Say what you will, but he was booted out over the "J" question.