Civil Rights and Liberties are not always complementary protections for citizens. Sometimes they can conflict. In the very interesting case of the Boy Scouts of America v. Dale (2000), the Supreme Court had the task of balancing First Amendment protections for free association against the civil rights protections provided under the laws of the State of New Jersey against discrimination.
As you can gather from the case summary, as well as for the longer “syllabus” of the case, the issue was whether the Boy Scouts could legally discriminate against homosexuals. On the one hand, as a private organization, the Boy Scouts have the right to determine their criteria for membership. On the other hand, the State of New Jersey has the power to pass laws forbidding discrimination on the basis of sexual orientation.