In his famous letter from Birmingham Jail, Martin Luther King, Jr.'s wrote: "One has not only a legal but a moral responsibility to obey just laws. Conversely, one has a moral responsibility to disobey unjust laws."
King wasn't encouraging us to break laws just because they were wrong and unjust. He had a purpose in mind and that purpose was to bring about change.
Similarly, when injustices are allowed under the law, we have a moral responsibility to seek to change those laws.
Our history is replete with many examples of bad laws that were challenged and changed. These have included outdated laws, some which allowed gross injustices such as slavery to exist with the blessing of the state, and others that limited or even prevented basic human rights such as the freedom to marry whomsoever you may choose.
Something may not be "against the law," but if it is wrong it should and must be stopped. For better or worse, in the modern world our only source of redress is generally an appeal to the ultimate authority wherever we are, which is usually the central government of the state or country in which we live.