text: The Old Catholics ordain women. The Old Catholics and PNCC allow for artificial contraception. Whether they started out as left wing schisms or got there further down the line is another question, but today those groups are on the left of the Catholic Church. 
  
  SSPX are not sedevacantist, you are thinking of SSPV and CMRI.  Whatever SSPX situation is, they are in an irregular canonical status which isn't the same as schism. Why would their priests receive faculties to hear confessions if they were in schism?  I wonder who you have in mind when you speak of a "host of movements and associations that are not formally schismatic, but advance reactionary ideology in the church and society."