Does Shakespeare create the characters of Lord and Lady Montague to be just awful people? Are they stage villains? Or does he paint them to be humans with normal human emotions who sometimes say things they don't mean out of anger?

This is only a short answer space. I think the parents on both sides are meant to represent the nobility of the time. They are pretty clueless about their own children. Indeed, Lady Capulet relies on Nurse to parent Juliet and Montague constantly has to ask Romeo's friends on how his son is doing. They are not bad people more than wrapped up in their own lavish lifestyles and silly feud.