FWIW, I agree that 'factionalism' is a far better term than tribalism. In fact, I am surprised that this has not been pointed out before - as it happens, I think I have actually been using 'factionalism' (and 'faction') consistently to mean what others on this site seem to call 'tribalism', although I am not going to take any credit for this. Factionalism is the accepted term in politics and political science, and the term 'tribalism' (also, 'neotribalism', or 'new tribalism') has other uses, for instance advocacy of small, self-contained communities (not exceeding Dunbar's number of about 150 members) focused on a dense social network and relative egalitarianism.
Various people (including Konkvistador who has been talking about it the most) have launched their blog More Right
"A group blog, More Right is a place to discuss the many things that are touched by politics that we prefer wouldn’t be, as well as right wing ideas in general. It grew out of the correspondences among like minded people in late 2012, who first began their journey studying the findings of modern cognitive science on the failings of human reasoning and ended it reading serious 19th century gentlemen denouncing democracy. Surveying modernity, we found cracks in its façade. Findings and seemingly correct ideas, carefully bolted down and hidden, met with disapproving stares and inarticulate denunciation when unearthed. This only whetted our appetites. Proceeding from the surface to the foundations, we found them lacking. This is reflected in the spirit of the site."