This is worth thinking about. Usually discussions of conscience don’t bring to the fore the question of if the person has a conscience that is telling them they must act, and the Church says not, or if the person has a conscience that is telling them it is okay to act, and the Church says not.
If it is a case of you think it would be okay to act, but the Church says otherwise, then don’t act. That is in accordance with your conscience.
Unfortunately, some people find themselves in the other situation. I’m surprised that the common advice then is to break your conscience. I disagree with that. In fact, I find it hard to understand a situation where your conscience has already ruled on the matter and then you go on and consider the Church teaching after that, at least for a well-informed Catholic. Whatever the Church teaches would be included in the deliberations prior to the ruling of the conscience. If you are calling something the ruling of your conscience, then that is what it is. You are done considering. There is no considering afterwards, otherwise you hadn’t decided yet, and so your conscience had not yet ruled on the matter.
The only way that this common advice makes sense to me is if they are using a different definition for conscience. Maybe they mean “conscience” is how you feel about the situation or something. IF that is the case, then the advice makes perfect sense. I tend to think of “conscience” as your last, best judgment of what is right in the situation. (ie, after all factors are duly considered). Clearly you ought to follow such a judgment (and yes, the judgment could be erroneous, and even could be culpably erroneous, and lead to harm). It is, what do you call it, almost vacuously true.
note: I’m trying to use both meanings of “conscience” in this post, hoping it will be clear which I mean at each point.