Scholars of the law and of political philosophy draw an important distinction that is directly applicable to answering this question. They distinguish between “the Rule of Law” and “a rule of law.” The former is an abstract concept that pertains to the overall operations of an entity, often a nation, that advocates adhering to the law. This must be separated from individual laws that members of that entity are expected to follow. As the question posed conflates these two ideas, they must be analytically separated to answer it fully.
Within a society governed by the Rule of Law, all individuals must agree to abide by that fundamental concept. This means in part that even if they disagree with a specific law, they must follow it as long as it remains in force. But it also means that they may, and should, take advantage of the existing mechanisms to try to change laws that they believe are unjust or otherwise run contrary to the general good.
When individuals do not adhere to this principle and willfully take illegal actions, a wide variety of situations can result. One manifestation can be lack of respect for those who are charged to uphold the law, such as the police and the courts. Individuals who lack confidence in the institutions or people who work in them are unlikely to report crimes, which allows criminals to operate without fear and may tend to increase the number of crimes committed. Alternate controlling bodies (e.g., vigilantes) may arise to usurp the role of the disrespected institutions. In situations of complete disregard for the Rule of Law, a society may further deteriorate into lawlessness or anarchy—that is, the absence of Rule of Law.