It is my understanding that Catholic laypeople are not specifically prohibited from attending Mass at an SSPX chapel,
and that such Masses do fulfill a Catholic’s Sunday obligation to attend Mass. The Catholic must not participate in the SSPX’s “schismatic attitude,” or intend to support dissent from Church teaching, or anything like that. If the layperson’s intentions are pure (e…g., she just really wants to attend a traditional Latin Mass and the SSPX are the only people offering one nearby), she is not specifically prohibited from attending.
Of course, that is not to say that it is morally right to attend SSPX Masses.It is just to say that it is left up to individual Catholics’
prudential judgment whether it is right or not to attend an SSPX Mass. I would not attend an SSPX Mass, because I would not want to give any level of support to Catholics who are systematically disobedient to the Church despite being exactly the sort of Catholics who should know better. Nevertheless, your prudential judgment might be different.
That particular claim I myself found on what I thought was the SSPX’s official website. I’ll see if I can dig it up again. Of course, the claim (as I remember it) is that it is grave matter to attend an OF Mass, but only a mortal sin if the Catholic in question has a sufficient understanding (full knowledge) of what he’s doing.
EDIT: Upon reflection, I withdrawal my claim that the SSPX generally holds it is a mortal sin to attend the novus ordo, on account of I can’t find the article I was thinking of. I think it may have been this archived thing:
archives.sspx.org/SSPX_FAQs/q5_novus_ordo_missae.htm
But it does not seem to say exactly what I thought it said.