It's impractical to not mention your name; it's trivially easy to not mention membership in a student organization. As such, including the membership signals 'I want you to know this' in a way the name doesn't.
Rather than expect applicants to take measures to whitewash their résumés (which also gives an advantage to those applicants whose extracurriculars are already "generic," i.e. upper-class and white), it seems we should be educating employers to be aware of their biases when reading these résumés, and teaching strategies for overcoming them.
Someone who deliberately and unnecessarily provides that information unasked for is puncturing that protection.
Now, I don't hire people, but this seems to me like a perfectly rational reason to be annoyed to know your applicants sexuality that has little to do with personal bias.