Extract from Catholic Encyclopedia article on heresy
newadvent.org/cathen/07256b.htm#REF_II
"…heretical tenets may be ignorance of the true creed, erroneous judgment, imperfect apprehension and comprehension of dogmas: in none of these does the will play an appreciable part, wherefore one of the necessary conditions of sinfulness–free choice–is wanting and such heresy is merely
objective, or
material. On the other hand the will may freely incline the intellect to adhere to tenets declared false by the Divine teaching authority of the Church. The impelling motives are many: intellectual pride or exaggerated reliance on one’s own insight; the illusions of religious zeal; the allurements of political or ecclesiastical power; the ties of material interests and personal status; and perhaps others more dishonourable. Heresy thus willed is imputable to the subject and carries with it a varying degree of guilt; it is called
formal…
Later:
"Towards material heretics her conduct is ruled by the saying of St. Augustine: “Those are by no means to be accounted heretics who do not defend their false and perverse opinions with pertinacious zeal (
animositas), especially when their error is not the fruit of audacious presumption but has been communicated to them by seduced and lapsed parents, and when they are seeking the truth with cautious solicitude and ready to be corrected”
It is necessary to continue in filial obedience to one’s rightful bishop, even if they have unknowingly lapsed into material heresy. What other link to the Holy See will you have if not through your bishop? (still I would suggest moving if you can)
But again, it makes no sense to follow them into material heresy, one can disobey their heresy.
One has to be prudent with obedience:
Catholic Encyclopedia article on Obedience.
"On the other hand the obligation to obedience to superiors under God admits of limitations. We are not bound to obey a superior in a matter which does not fall within the limits of his preceptive power. Thus for instance parents although entitled beyond question of the submission of their children until they become of age, have no right to command them to marry. Neither can a superior claim our obedience in contravention to the dispositions of higher authority. Hence, notably, we cannot heed the behests of any human power no matter how venerable or undisputed as against the ordinances of God. "