The action is:
Court clerks refusing to issue marriage licenses to same-sex couples.
Grassroots activism is a movement of people, who are passionate about a cause and harnessing the power of their conviction to push for a different outcome. This answer is a direct reference to the case of Sandra Davis, a Kentucky country Clerk that refused to issue same-sex marriage licenses due to her own personal convictions and in the name of "religious liberty". Her initiative was purely personal and was not the result of organized political efforts.