I’m part of a professional library association that is a 501(c)(3), like the American Library Association, Association for College and Research Libraries, and the Society for American Archivists. Occasionally, the group issues statements in solidarity with various groups, for instance, in protest of police violence against Black people and against Anti-Asian violence.
This is an area that (literally) tears groups apart.
There is no one right answer to this, but countless examples show that the process for arriving at an answer is just as important as the decision to issue a statement (or not) of support (or opposition).