The key is in looking at the card text.
If a card becomes "unaffected" by other effects, this means any effect that would affect the card in question, not effects or conditions that would apply to other cards or players.
Threatening Roar, Dimension Gate, etc do not affect specific monsters. Waboku does, but it affects your monsters, not the opponent's. An opponent's Omega could not use its effect to be immune to Waboku and kill one of your monsters by battle, because Waboku is not affecting that Omega.
Messenger of peace is vice versa. It does affect Constellars, so Omega can get around this.