Surely if there ever was a perfect catch-all phrase, it is "teachings-of-the-Church". It includes everything from defined dogmas, items in the Apostle's Creed, 1752 Canon laws, opinions of the Pope (like steam locomotives are the work of the devil), every one of the 2865 items in the Catechism, to the thoughts of cranky old bishops like Burke and Molino. It has become a universal cliche of the hierarchy to discourage dissent. Falling into the same catch-all basket of against "The Teachings of the Church" are those who disagree with pre-Vatican II liturgical norms and language, contraception, mandatory celibacy for priests, collective bargaining, just war and torture, women's ordination, slavery, same sex unions, the resurrection of Jesus, the nature of the Trinity, and if God really exists. Note that some "Teachings of the Church" are slippery, time-bound, and culturally-colored.
At stake here is the power and authority, originating from the community of the Church and appropriated by unelected leaders to set the rules for who is in and who is out. By voting a certain way, you could be considered "out" according to "The Teachings of the Church". By not behaving/believing according to the bishop's instruction, you are obviously against the Teaching of the Church.
Some (bishops?) believe good teaching is the attempt to influence, even coerce, the faithful into believing what is being taught. But the criteria for effective teaching involves rather if the teaching makes sense and is received by the faithful. If you do not accept that all contraception is sinful, or legalizing same-sex unions are wrong, or only men can be ordained, or contributors should have a say in how their money is spent and who should be responsible, or the language of prayer should be strange or contorted, or bishops should tell us how to vote, you are dissenting against "the teachings of the Church".
Without careful and intelligent scrutiny, accepting every "teaching of the Church" is similar to checking the box "I agree" to observe every privacy/usage rule for downloading new software/ upgrades. Study the reasoning behind Church teachings, consult and observe how your Catholic community receives them, and judge for yourself. Follow your own well-formed conscience, as fallible as it may be.