This is so widely known I’m surprised you ask, but consider for one thing, Williamson, one of the founders, excommunicated and kicked out of SSPX for his extreme, blatant and oft-stated views against Jews.
The SSPX also rejects, and sometimes they homilize on this, Nostrae Aetate.
Nostra Aetate contains heresy. I denies the dogma of “Extra Ecclesiam Nulla Salus”.