I have a question, which I do not ask rhetorically, since I really don't know the answer. Does the "mainstream" of the traditionalist movement openly and clearly condemn antisemitism? For example, have the bishops of the SSPX issued statements or pastoral letters plainly condemning antisemitism? And have they taken steps to purge whatever antisemites may be in leadership positions? have they attacked the "Jews and freemasons" talk that is popular at tha radical fringe?
We often make the point that Muslims, if they are sincere about Islam being a "religion of peace", should be louder in denouncing jihadism and Islamofascism. By the same token, the traditionalists should take the lead in denouncing antisemitism.
On the contrary, they're often in the vanguard of those stoking these fires. Take for instance this quote from Bishop Richard Williamson of the SSPX:
"God puts in men's hands the "Protocols of the Sages of Sion" and the "Rakovsky Interview", if men want to know the truth, but few do."
Taken from Bishop Williamson's Letter Archive, May 2000
It's clear that this SSPX bishop considers the Protocols to be an excellent and reliable text. It's also seems quite likely that he has promoted this view, at least to some extent, within the Society.
I don't see why the SSPX would have to - these other people, such as Gruner, etc. aren't members of it. To my knowledge, some of them aren't even "traditionalists" in the sense that this word is used in the Catholic Church, usually to refer to liturgical traditionalists. The claim of "antisemitism," based on the words of verious individuals, is being used as a very wide brush to tar a group that is hated by the leftists in (and outside of) the Church.
I'd be equally interested in seeing some of the pro-Palestinian leftist clergy in the ME apologize for some of the anti-Semitic remarks that occasionally make it into the press, but they'll never do that. Furthermore, you'll never hear the left (which is anti-Semitic itself) asking them to do so.