Again, as long as Brother Nathanael isn't officially accepted into SSPX, it wouldn't reflect badly on the SSPX. Pretty much anyone can just show up at their chapels. I'm basically a sedeprivationist Feeneyite who believes that Prevost is no more pope than my pet cat is, and I will show up from time to time at SSPX chapels.
Now, if the Conciliars try to pressure them into "condemning" what Brother Nathanael says, they could easily turn the Modernists' claims about their status by saying that "we have no authority to condemn anyone or anyting, since we lack ordinary jurisdiction in the Church."