It is popular in certain Catholic circles to derisively refer to the SSPX as Protestants with the liberal use of sneering adjectives attached.
It seems plain to me that most of this same sneering class would never actually speak that way of actual protestants, as that would be most un-ecumenical.
While I have been critical of the SSPX, I still long for their return to full communion and recognition. I came across a very interesting editorial on the sspx.org website (ht eponymous flower) by Fr. Michel Simoulin that might be food for thought for those who think that the SSPX, as a whole, WANT to be separate.
I quote in part:
And now we must open our eyes to another danger, that is not hypothetical, but very real: that of no longer wishing to return to our legitimate place among the societies recognized by Rome, of losing the desire for the Church and for Rome. No longer desiring a normal relation with Rome and the Church is a shadow of the schismatic spirit. We have been living in independence from the Pope and the Bishops for a very long time, as if that were normal. We pretend to defend the doctrine, but we all run the risk of establishing a chosen doctrine, abandoning certain dogmas, those that bother us, especially those concerning the primacy of Peter. We all run the risk of becoming accustomed to the abnormal, of living in a comfortable situation, as if it were right and in conformity with the spirit of the Church. The Pope and the bishops are little by little confined to the realm of the beings “of reason”, with no influence on concrete life; Rome is no more than a pilgrimage site, and the Church is a Mystical Body with Jesus Christ for a head, the Holy Ghost for a soul, and the “Trads” for members. Our priests can quickly become gurus. Everyone could be a Pope with his Denzinger in hand, and every father of every family could be the Pope of his family. In these conditions, our children would no longer have any idea of what the real Church is in its full incarnation, from head to members, in all the realities of daily life.
I think this is very healthy introspection and an indication that while still separated, they are our Catholic brothers.
I urge you to read the whole thing. It is a quite well balanced assessment of the current situation.