Revoltingly is how you say that something is done in a disgusting way, or that the unpleasant feeling is very strong: the meat smelled revoltingly bad; he behaved revoltingly towards the waiter. It belongs to the “makes you want to turn away” sense of revolting, not to politics. You would not use it to mean “in a way that starts a revolution.” It is a heavy, emotional adverb. In careful writing it can sound a little old or stage-like; in speech people still reach for it when they want to show they are really put off, not just mildly annoyed.