I think what we need here --- and the Catholic and Anglicans may help us to get it --- is an adequate definition of what kind of conscience we're talking about.
A lot of people use conscience loosely to mean opinion, or instinct, or even a purely individual inclination or preference. The word itself indicates that it's not a purely individual thing ("con-science" means to "know-with," i.e. to know with the other people of God throughout the ages -- to have the mind of the Church.)
Before it has rights, the conscience has duties: The duties are to be formed and informed. Over the years, your conscience has to be formed by virtue, by habitual upright behavior, by thinking, accepting, and internalizing God's laws. Informed means that the person has made an effort to learn the moral principles which apply, plus the real factual basis of the situation.
Conscience is a student, not a teacher.
Not exactly
Jer 31:33 "But this is the covenant which I will make with the house of Israel after those days," declares the LORD, "I will put My law within them and on their heart I will write it; and I will be their God, and they shall be My people.
Rom 2:14 For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves,
Rom 2:15 in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them,
Rom 2:16 on the day when, according to my gospel, God will judge the secrets of men through Christ Jesus.
The homosexual agenda must be learned. The Law of God is inherent.... and inerrant.