There isn't an in-game way to do this, but if you have Steam Cloudsync disabled you can go to the My Games/LegendaryHeroes/Race folder, find the faction you want to delete or edit (it will be the XML file called "Faction_YourFactionName"), and do what you want to it. If you want to be rid of it, be advised that it used to be that as long as Steam Cloudsync was enabled you couldn't be rid of the faction because it would be restored whenever the game synced to the cloud; since I disabled that for this game a while ago I couldn't tell you if that were still the case. If you want to edit the file, you'll need a text editor like NotePad, WordPad, or NotePad++, and you might want to have a reference XML document (say, the Altar faction XML file) in case you delete tags you needed while manually editing the file.
