The Ku Klux Klan (KKK) violently threatened the political rights that African-Americans had achieved when the Civil War ended, so they were purposely breaking the law and going against the national values of the time. So the answer is no, they, and other groups like them, should not have the right to exist in the US.
Explanation:
Should we allow the right to exist of people who are against the political rights of African Americans? Of course! Everyone is entitled to their opinion, even if they tend to discriminate against people. However, there´s a key difference between opposing a public policy and committing violent acts to enforce our ideas against the law, and the latter should not be allowed.
