Many civil rights protections are simply in place to make sure that people are all given the same rights, regardless of factors outside of their control.
Your civil rights are your personal liberties -- your ability to live a lawful life that is free of harassment, discrimination, persecution, or intrusion from others (including the police and the government). These are rights that are seen as belonging to everyone -- no matter their status in society.
California protects its residents from various forms of discrimination under its civil rights laws, including housing discrimination.
Your right to peacefully demonstrate for a cause is guaranteed by the Constitution. You have the right to free speech. But occasionally, when an issue is front and center and may even be a protest against the police, rights can be trampled on. Tempers can flare and violence may break out; police officers may begin making arrests or using crowd control measures, including the illegal use of force.
Every so often, you'll see citizens claiming they've been falsely arrested by the police. In some cases, they just mean that they are innocent but have been arrested anyway; this does not necessarily mean that the law was broken.
"You have the right to remain silent. Anything you say can and will be used against you in a court of law. You have the right to an attorney. If you cannot afford an attorney, one will be appointed for you." This statement may seem like something you only hear on TV dramas and police procedurals. But it is, in fact, one of the most important statements that relates to our civil rights. It is the Miranda Warning, a required statement that the police must read to you when they arrest you.