The V2 authorities, your local bishop and the popes have always said the SSPX is in schism.
Firstly, any local bishop, or even archbishop is not a vatican official, they have no training or authority to condemn anyone a schismatic. Any such condemnation requires due process which does not happen at the diocesan level, but only when roman officials are involved, whose job it is to study such circuмstances. So any comments by local bishops, outside of saying that the 4 bishops are excommunicated (which rome has made clear...but has since recinded), are incorrect. Even Bishop Hoyos, I believe, has said multiple times in public interviews that the sspx is not schismatic. He has only ever said they are "not in full communion with rome" which phrase "full communion" is novel, ambiguous and imprecise. Modernists at their best!
In regards to roman officials, it depends on the reason for why they would label the sspx schismatic. The only reason they ever bring up are the consecrations of '88. New-rome has NEVER said that the masses, sacraments, etc are schismatic. They only mention the 4 bishops and their 'disobedience'.
So the sspx bishops are arguably schismatic, though they have never been formally called so by rome, so the argument is weak. (If one assumes that there was not an 'emergency reason' to provide the sacraments, as allowed/encouraged by canon law, one could argue their
consecratory act was schismatic. But since there was an emergency reason, then that argument is moot. The local bishops only made such extreme accusations of schism and excommunication to keep the "V2 faithful" from waking up - to shock them - so that the sspx wouldn't grow. It was mostly a PR campaign to keep the sheeple in line. V2 knows that the sspx's masses and sacraments aren't schismatic and has never formally said so.)
The main purpose of the sspx (and tradition), i.e. to keep the Faith by practicing the pre-V2 religion, is not schismatic, only the 4 bishops are possibly schismatic. BIG DIFFERENCE.
And here's why the 4 bishops are not in schism, or why it doesn't affect the laity who attend the sspx:
1. SALUS ANIMARUM SUPREMA LEX - "The salvation of souls is the highest law". This means that the Church makes very, VERY many allowances so that catholics can make it to heaven. This is why She allows even excommunicated clergy to provide the sacraments, in danger of death, or when no one else is available.
2. Speaking of the 4 excommunicated bishops (and even their priests). The code of 1917 canon law allows for the providing of the sacraments, if there is no one else to provide. Can trads receive the old rites and a non-indult TLM from their local diocese? Nope. So, the sspx (and all other traditional priests) are fulfiling a need and are allowed by canon law to do so.
Canon 2261.2-3, 1917 Code of Canon Law: “… The Faithful may for any just cause ask The Sacraments or Sacramentals of one who is excommunicated, ESPECIALLY, IF there is no one else to give them (c. 2261.2).3. ‘Necessity makes licit what is illicit.’ Pope Gregory IX: ‘It is true that one sins against the rule who adheres to the letter and leaves aside the spirit’