From what i see, the Society of St Pius X (SSPX), which effectively broke with Rome in 1988 in a protest against the liberal changes that followed Vatican2 (and which mainline RCs say were clarifications), has been moving toward " possible reconciliation with Rome" (there that term used again by Catholic source), but which might lead to the group splitting apart. Another main schismatic Catholic group, the sedevacantists, would also be opposed to that.
Then there are those liberals in communion with Rome who,
fear that the reconciliation of the SSPX is a move in a sinister plot to “turn back the clock” to a pre-Vatican II Church.
The author of that sentence is a conciliatory one, who comments,
"Progressives and traditionalists alike have produced tenable yet also mutually exclusive interpretations of liturgical law based on the torrent of verbiage which has issued from the Vatican in the post-Vatican II period."
There are those who argue that the SSPX “should not be accepted back into the Church” because “they still reject Vatican II.” But should they be excommunicated, anathematized and excoriated all in the name of a Council which intentionally avoided excommunications, anathemas and excoriations, even if some SSPX adherents would like to see excommunications, anathemas and excoriations thundered from the Throne of Peter?
More: http://www.chantcafe.com/2012/05/sspx-who-cares.html
Do they even know if they’re coming or going?