Schism can be due to either 1) Refusing subjection/submissoin to and communion with the Holy See or 2) refusing communion with other Catholics.
Per 1 -- If Bergoglio is the Pope, a refusal of submission would constitute schism ... unless the individual entertains some well-founded doubt about the legitimacy of Bergoglio (per the Canonists). Now, even though some groups hold that Bergoglio is pope, many entertain the possibility that he might not be (we've heard that from +Lefebvre, and even +Williamson and others), at which point, lacking the requisite dogmatic-fact-certainty regarding Bergoglio's papacy, that would absolve someone of schism per those Canonists. Dogmatic Sedeplenists who refuse submission to and communion with Bergoglio would be schismatic.
Per 2 -- Some Trads dogmatize their conclusions / theories / positions about various subjects that are in fact not dogmatically certain and treat those who do not adhere to their positions as if they were non-Catholics, refusing Communion with them (e.g. priests refusing Sacraments). By refusing communion with other Catholics, they too can be in schism (if they're wrong about their conclusions, which in most cases they are). So, for instance, SSPV in treating CMRI and Feeneyites as non-Catholics (refusing them Communion), or the radical Pro-EENS crowd, meaning those who hold that anyone who believes in BoD is a heretic (even if the position is articulated in a way that the Church has tolerated and accepted, e.g. the position of some of the Church Doctors. There is a distinction, too, where one can argue that a cetain POSITION is objectively heretical, but since the Church has not defined it clearly enough or weighed in on it, they still consider those who adhere to it Catholics, because the Church has not concluded otherwise. So, for instance, if I were a Thomist priest, I might still argue that Molinism is objectively heretical, but since the Church said we should still consider those who adhere to it Catholic, I would still give Holy Communion to Molinists. One might HAVE argued before the definition of papal infallibility or the Immaculate Conception, that these were objectively dogmas, but couldn't refuse communion with those who didn't agree with that ... until it was clearly defined by the Church. In point of fact, they'd be right, since all dogmas were always dogmas, having all been revealed in the Deposit of Faith before the death of the last Apostle (St. John) ... but those who denied them would not be formal heretics (guilty of heresy) until the Church defined it with sufficient clarity to end all doubt and establish the certainty of faith regarding that conclusion. Consequently, while one might ARGUE that a certain position is OBJECTIVELY heretical, one cannot refuse communion with (or, in the case of priests/bishops, the Sacraments to) those who do not hold your position.
So, many of the "dogmatic" positions, whether dogmatic R&R (while remaining Trad and refusing submmission to Bergoglio), meaning where it's dogmatically certain (dogmatic fact) that Bergoglio is pope, or else dogmatic SVism or dogmatic anti-BoDism, meaning that they'd refuse communion with thoes who disagree with their as-yet-not-defined conclusions ... those would be schismatic. Unfortunately, many of the Trad positions have been illegitimately elevated to the level of dogma, and I find that there's only one that is a legitimate point of dogmatic contention, namely, the nature of the Church and of the papacy and the Magisterium where it pertains to the indefectibility of the Church.
I'm working on an essay on my Substack entitled "Dogmatic Indefectibilism" to lay all this out. I actually have a half dozen (or more) essays in various states of completion on there, and have to "pull the trigger" on some of them. While I can rattle off posts like this in a minute, I tend to be a bit over-perfectionist about the stuff there, trying to make sure they're very polished ... and I think it's a case of the perfect being the enemy of the good.
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