Many people want free speech, as a concept, ideal and aspect of living a safe and fulfilling life. When they are being deprived of that right, if they are in the USA, the people depriving them are quick to point out that the first amendment doesn't protect them... but that's completely irrelevant.
As an example, imagine the constitution had a right which said "The federal government will not murder you". Then today, some people are murdering everyone they dislike, and when some people point out "we're afraid of getting murdered and want to live in a society where there isn't murder" and immediately internet commentary is full of people responding "Actually, you only have a right to not be murdered by the federal government, you're confused about how your murder rights work".
It's not that the oppressed are confused about what's written in the Bill of Rights, it's that they care about the underlying ideal in a broad and practical way.