A priest may disagree with certain basic doctrines of the Catholic ministry such as the immaculate conception, the papal magisterium or purgatory?
It makes no sense for a Catholic priest to disagree with Marian worship, the papal magisterium, purgatory, etc, while continuing to remain in the Catholic Church, that imposes those doctrines. Let us not forget that a priest is not a simple frequenter of the Catholic Church, who may very well continue to frequent it even if he does not believe in the aforementioned doctrines. A priest has the obligation to teach, preach the doctrine, cure souls, and what sense would it be to teach the opposite of what Chiesche represents? And it is precisely from these differences that the veteran Catholics were born, who do not believe in those typically Roman doctrines while continuing to remain substantially Catholic, both in the ecclesiastical organization, than liturgical, what a doctrinal. It is more consistent for a priest to break away from the Roman church and adhere to this denomination, than not to continue lying to himself and to others.
For further information: http://www.chiesaveterocattolica.it/