This isn't really a separate answer, but rather to allow me to elaborate slightly on @slhck's suggestion of using the Stylish Firefox extension for anyone else interested in doing it. After downloading and installing the add-on, I manually added the following style and named it NoTagMenu:

@namespace url(http://www.w3.org/1999/xhtml);

@-moz-document domain("superuser.com"), domain("stackoverflow.com")  {

/* ccs rule */
#tag-menu {
  display: none;
}

As you can see, I have it also applied to the stackoverflow domain, which has the same issue (no surprise).