It is morally right to break an immoral law in my view, now an unjust law could conceivably not be immoral if it dealt with matters not pertaining to morality but if an unjust law were immoral than it would be moral to break it. Who enacts the law is irrelevant to this unless one subscribes to the view that any law which is enacted by a political process one supports is always justified.
The reason I consider a law to not necessarily be moral even if enacted by a political system I support is because I believe there is such a thing as Divine Law which is established by God and which supersedes any laws passed by people. I don't support the view for example that because a law may be passed via popular consent that it is right. Laws may be passed via the popular will that are immoral and it is moral to disobey and undermine them.
The advantage of codified written law is that it provides an identical standard by which we can judge the actions of every person in a society uniformly. I have yet to see any sort of "divine law" pass this test. There is no consensus among believers in the divine as to what god does and does not condone. The subjectivity of belief does not only exist between faiths, it exists within them. So if you are arguing that you have the right to break the law because it violates your personal interpretation of the divine law, then you must logically extend that right to everyone else in the society. The end result of this line of thinking is indistinguishable from anarchy.
Yes I do believe everyone should only follow a law if it agrees with their moral views, that's why I believe a society where you have people with fundamentally different views of what is moral or immoral is destined to fail as you might have one group of people considering one thing moral and another set consider that thing immoral, only a society where everyone has the same basic worldview is capable of functioning in the long run. The experience of history is societies where you have different worldviews on fundamental matters present tend to fail eventually.