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So the two sides throw the term "schismatic" at each other, even though in reality neither side is in schism, in order to cow the other party and strengthen their own position?

Well, thanks for taking the time to answer the question of a Baptist who happened to stray in here. ;^)

Those who reject the authority of the Pope and of officially-appointed bishops, who, as it were, set up and direct their own Church, would be considered to be in some type of "schism." They dispute the authoritative structure of the official Church over such things as how to conduct the Mass, the central sacramental rite.

There is some more about "schism" on these links:

http://www.newadvent.org/summa/303900.htm

http://lphrc.org/rmk/trid.html

Apparently, some people have the exaggerated understanding of the pope's or bishops' authority that if they told people to go jump in a lake, they would be bound by faith to be obedient to such an absurd demand. This is not actually the case. They are limited by the articles of faith, the revealed doctrines of the Church, and by tradition, in terms of what they can reasonably request of the Catholic faithful. They couldn't command everyone to accept Krishna, Buddha, or Mohammed all of the sudden as the equals of Christ. Likewise, they can't force people on faith to accept Rock music or abstract modern art or open homosexualism.