Take callow and callous. Callow means "inexperienced, immature;" it's also frequently used to mean "gullible, naive." Callous means "displaying an insensitive, unsympathetic or cruel attitude."
People who believe rumors that current proposals for health care reform include having government officials force end-of-life decisions on people are callow.
People who think it's no big deal that millions of Americans go without any health insurance so long as they have theirs are callous.
Interestingly, these words have distinct roots as well. Callow derives from the Old English term calu meaning "bald," and probably came from the Latin term for bald, calvus. The word originally referred to an unfledged (hence bald) bird and was eventually extended to any immature thing. Callous comes from the Latin callosus and ultimately callum meaning "hard skin." The term shouldn't be confused with callus, the word for a hardened spot of skin, like you might have on the balls of your feet if you have a job that keeps you hopping all day.