Cardinal Newman wrote of conscience as a voice of God heard in the heart; a voice that prompts us to act in one way rather than another and a voice that, after we have acted, provides a sanction as to the rightness or wrongness of what we have done. He is also clear that conscience does not act as a judge of the truth or otherwise of what we might believe, but rather that it bears directly on our action, on what we do (or do not do). This is not to suggest that the business of "following our conscience" is an irrational thing; on the contrary, our responding to the prompting of conscience is a profoundly reasonable and reasoned act, rooted in the urge to put our actions in conformity with what we know and understand to be morally true and just.
Understood in this way, a theory of conscience does not give Catholics the freedom to act in disregard of Catholic teaching. Its demand is quite the oppositie. It asks us to put into effect in our actions what we know from the teaching of the Church is morally true and just (and the Catechism of the Catholic Church provides an authoritative and contemporary statement of what that teaching says). For the lay faithful, whose task is to live their Christian lives "in the world", this demand of conscience has a particular relevance to their state of life in the Church and the world.
There are circumstances where the demands of conscience impose an absolute, and the question in those sorts of circumstances is more one of courage than one of decision. But there are also circumstances where a potential course of action exists in a relation to Catholic teaching but where different choices are possible that do not involve acting against Catholic teaching. So, for example, many Christians feel able to be members of political parties some of whose policies they do not support, while others do not feel able to join a mainstream political party. And among Catholics, some feel called to engage in one particular area of apostolic activity when others feel that they are called to engage in another field - this is where the voice of conscience has an individual and vocational character.
The question of political resignation - or of abdication - does I think come in to this latter style. The core questions that impinge on conscience in these circumstances are, firstly, that we should not support or collaborate in a policy that we believe to be morally evil and secondly, that others should not believe that we do support that policy when we believe it to be evil. A resignation - or abdication - could very easily be one among a range of courses of action that could meet the demands set by conscience, but not be the only such course of action. Both objective principle and prudential judgement are in play, and my view is that it is in circumstances like these that we can genuinely talk about a "freedom of conscience". Many political situations are ones where different people in a party (or, in my case, a trade union) hold different views on a matter, and the nature of membership organisations such as these is that a certain pluralism with regard to policies is a recognised feature of their landscape. Some people will make the judgement of conscience that they can remain "in", recognising that this pluralism means that their membership is not to be equated with adherence to each and every policy; whilst another person might make a judgement that continued membership does imply support for a policy they find morally unjust, and that therefore resignation - or abdication - is called for.
All of which is by way of explaining why I am distinctly uncomfortable with the statement that "Queen Elizabeth II, as a Christian monarch, should have made it clear that she would abdicate the British throne if the House of Commons voted to legalise abortion in 1967". It might be the judgement of conscience that Deacon Nick would have liked her to make; but I think in public discussion we should recognise the broader possibilities.
Resignations are a rather more subtle thing than first meets the eye. And, yes, I do have some experience of my own to draw on.