It's more accurate to say "individuals don't cease to have rights just because they act through a corporation." There are some rights that don't make sense applied to a corporation, and people don't have those rights when acting through a corporate form. (E.g. the Fifth Amendment right against self-incrimination.) But for most rights, deeming them inapplicable when people are acting as a corporation would be an extremely effective way to eviscerate the underlying right.
The ACLU, Sierra Club, etc., are all corporations. They need to be corporations in order to enable their fund-raising and nationwide scope of activities. Nobody really thinks the ACLU shouldn't have the right to free speech. (Note: The ACLU was on the winning side in Citizens United.) What people are opposed to is the content of the speech that some people speak when acting through the corporate form. (Citizens United was about a movie critical of Hilary Clinton.) But if free speech means anything, it means you can't single out speech based on content.
The ACLU, Sierra Club, etc., are all corporations. They need to be corporations in order to enable their fund-raising and nationwide scope of activities. Nobody really thinks the ACLU shouldn't have the right to free speech. (Note: The ACLU was on the winning side in Citizens United.) What people are opposed to is the content of the speech that some people speak when acting through the corporate form. (Citizens United was about a movie critical of Hilary Clinton.) But if free speech means anything, it means you can't single out speech based on content.