In the May 5, 1988 protocol that was signed by Archbishop Lefebvre and withdrawn the next day due to the delaying tactics for the episcopal consecrations:
4. We declare moreover that we will recognize the validity of the sacrifice of the Mass and of the sacraments celebrated with the intention of doing what the Church does and according to the rites in the typical editions of the missal and rituals of the sacraments promulgated by Popes Paul VI and John Paul II.
So the new rites are recognized as valid by Archbishop Lefebvre and the SSPX as long as they are validly celebrated according to the typical editions. However, to my knowledge, no SSPX priest or publication has publicly said that it is OK to attend the New Mass. It seems that Bishop Williamson and the Resistance faction associated with him are even more liberal with regards to the New Mass.
Archbishop Lefebvre only admitted to validity. Everyone should know that validity does NOT equal grace (see the Church's teaching on attendance at VALID Orthodox sacraments that nevertheless are not allowed). See also here for how +W and Johnson are wrong on this issue according to Church teaching. https://fsspx.news/en/content/32569
I've been around long enough to recall when both +W and Johnson used to say the opposite of what they are saying about grace in the New Mass. It's actually well docuмented, particularly in +W's case. Maybe the fight has gone out of him?