No. Because if the group cared enough they could make their own add-on to do just that. And it wouldn't need to go through Google to be installed for "members".

No. Because if the group cared enough they could make their own add-on to do just that. And it wouldn't need to go through Google to be installed for "members". "Is a member of a nazi-esque group" is not exclusive from "is tech literate enough to write browser add-ons". If you let others control your actions, even indirectly, you show them that they have power and control over you. Many tools that are beneficial are also "double-edged" and could be used for nefarious purposes. In most cases, they're better off existing than not.