Hawaiian's B717 interisland pilots, ties are optional. Island Air (before they closed doors), the pilots never wore ties (they weren't even issued ties... or a hat... or blazer). Wasn't Virgin America tie-less as well prior to the Alaska merger?
My current airline policy: The tie shall be worn unless both of the following conditions are met: Locally reported temperature 90°F (32°C) or greater. No more than the top button is unbuttoned when the tie is removed.