"Where Church authority remains fully true to her mission and where conscience becomes pure, the antinomy between freedom and constraint is dissolved." - Ratzinger
The Church offers clear teaching on conscience. When confused by media reports of what this bishop or even Pope Francis says regarding Catholic moral teaching, search out authentic Catholic teaching in the Catechism and the official teachings of the Magisterium. Pope John Paul II and Pope Benedict XVI wrote extensively on conscience, theology, and Church authority. A couple of examples here:
"... Saint Paul [who] tells us, that the pagans, even without the law, knew quite well what God expected of them (Rom 2:1- 16). The whole theory of salvation through ignorance breaks apart with this verse. There is present in man the truth that is not to be repulsed, that one truth of the creator which in the revelation of salvation history has also been put in writing. Man can see the truth of God from the fact of his creaturehood. Not to see it is guilt. It is not seen because man does not want to see it. The "no" of the will which hinders recognition is guilt. The fact that the signal lamp does not shine is the consequence of a deliberate looking away from that which we do not wish to see. - RatzingerBlessed Pope John Paul II.
32. Certain currents of modern thought have gone so far as to exalt freedom to such an extent that it becomes an absolute, which would then be the source of values. This is the direction taken by doctrines which have lost the sense of the transcendent or which are explicitly atheist. The individual conscience is accorded the status of a supreme tribunal of moral judgment which hands down categorical and infallible decisions about good and evil. To the affirmation that one has a duty to follow one's conscience is unduly added the affirmation that one's moral judgment is true merely by the fact that it has its origin in the conscience. But in this way the inescapable claims of truth disappear, yielding their place to a criterion of sincerity, authenticity and "being at peace with oneself", so much so that some have come to adopt a radically subjectivistic conception of moral judgment.
As is immediately evident, the crisis of truth is not unconnected with this development. Once the idea of a universal truth about the good, knowable by human reason, is lost, inevitably the notion of conscience also changes. - Veritatis Splendor
It is very important to know Catholic teaching on these issues. Don't look to secular media for what the Church teaches, and even beware Catholic social media.* Go to the source, the deposit of Faith: The Church.
*Fr. Z is the exception, here: