Say I have used Meereen to make Rhaegal immune to triggered effects. My opponent uses Maiden of Poisons to name Power. Rhaegal is my only Power icon.

Surely Meereen makes Rhaegal immune to this? There was a school of thought that since the wording on the text was for Maiden of Poison's controller to "name an icon type" and that I, as Rhaegal's controller, was forced to choose Rhaegal that Meereen's immunity would not cover it as it only covers "opponent's triggered effects" and the triggered effect was implemented by me, not an opponent.

Again, surely Meereen makes Rhaegal immune as the whole ability is a triggered effect triggered by an opponent?

OKTarg said:

The Maiden's full text is:

"Response: After you lose a challenge as the defender, choose a challenge icon. Then each opponent chooses 1 standing character he or she controls with that icon, if able. All chosen characters lose that icon until the end of the phase."

Remember also that immunity prevents two completely separate things:

1. Immune cards cannot be chosen as targets by what they are immune to.
2. Immune cards cannot be directly affected by what they are immune to, targeted or not.

So, here's what you ask yourself for Maiden of Poisons and Meereen-says-immune-to-opponent's-triggered-effects-Rhaegal:

1. Is any part of the resolution of Maiden of Poison's (triggered) Response effect trying to choose Rhaegal as a target?
2. Is any part of the resolution of Maiden of Poison's (triggered) Response effect trying to directly affect Rhaegal?

If the answer to either of those is "yes" (and the answer to both is, indeed, "yes"), the immunity stops it. Even if you could choose Rhaegal as your character as a power icon (you can't), he wouldn't lose it.

What the "school of thought" you describe is trying to do is over-extend the "indirect" or "secondary action" "loophole" in immunity. Say that I have a character that is immune to events. You use an event to give a character of yours Stealth. Can you attack with that character and use its event-granted stealth to bypass my event-immune character? Of course, because your event did not work directly on my immune character. It worked "indirectly" through a "secondary action." It changed your character, which then worked on my immune character.

The argument your "school of thought" is trying to make is that by Maiden of Poisons having its controller choose the icon type ("power" in your example), it is somehow not the Maiden's triggered Response effect that is targeting the character with the icon or removing it. But if it is not the Maiden's effect that is doing those things, what is? The player who chose the icon type? Clearly not.

So long as the immune character would be directly affected by the resolving character ability, it ignores the effect - no matter what the character ability does to a player at the same time.