So what do you do with Eastern Catholics who openly reject papal infallibility?
It's not clear to me whether it the teaching itself that they reject, or just misunderstanding/exaggerations of it.
EWTN speaks of the rejection of various omportant Roman Catholic teachings by the autonomous Catholic Churches.. Mildy expressed as you would expect and really not at all indicative of the massive dissent simmering in the Eastern Catholic Churches.
"Disputes among the indigenous
clergy and the immigrant Byzantine clergy have often resulted in whole
parishes leaving the Catholic communion to be received back into Orthodox
folds. (See the COMMENTS for the Carpatho-Ruthenians below.) Other
sources of disagreement are the Immaculate Conception, Papal Supremacy and
Infallibility, Purgatory, and the Filioque, and to a lesser extent
remarriage after divorce; in short, all the matters that remain primary
points of disagreement between Orthodox and Catholics. The terms of the
original agreement are clear that agreement with Rome on these matters is