Although Blue had control of the equality outpost at the start of the turn, Red took control of it during the turn. By the above rule, control of other outposts should have been resolved by breaking ties in favor of Red. Since at the end of the turn the "move opponent's card" outpost was a 2/2 tie, and Red was in control of the equality outpost at that point, control should have been resolved in favor of Red, not Blue.

rule cited "If the power allows the player to take control of another outpost, step 2 is repeated until all combos are exhausted."

I had the same thing happen to me. Table #426801086 Move #45+

Red played 3 to both sides empty outpost move opponent's card. Control move to red.

Red moves card from equality to move opponent's outpost, making move opponents' outpost equal and making equality switch from blue to red at the same time.

The game asked me to pick the first token to flip. I picked equality, thinking that I want that to process first so that the move opponent's card remains on red (equality in red's control). But as soon as I picked equality to flip to red, it also flipped move opponent's card to blue, which I believe to be a bug if I am understanding the rules correctly:

Page 8:
"RESOLUTION OF LOSSES AND CONQUESTS:
The order of resolution is freely chosen by the active player."

And further up on that page:
"In case of simultaneous conquests, the order of resolution of the conquest powers is freely chosen by the active player."

This seems clear to me, and thus is a bug, but I would love to hear what I may be missing if the developer or anyone else can clarify.

Thanks!

Same thing has happened to me multiple times. It seems that when you flip the equality outpost and another outpost at the same time ( not sure whether it is immediately before or immediately after or both) then oftentimes there is a glitch in ownership. For example, in two recent games I've flipped the equality outpost in order to trigger a tie to go my way, but the tied outpost remains in control of the opponent even though I now have possession of the equality outpost. Seems like the equality outpost is not having its logic tested again after the initial choice of "which outpost to flip next." Seems as though the equality outpost should be tested again at the end of every move to confirm that all ties are going to the correct player.

Similar here on #633037022.

A couple of moves in I moved an opponent card from the equality token (giving myself majority on that token) to another outpost where the scores are equal.

The system asked which outpost to resolve first. I chose the equality token. The equality flipped but then the new equal outpost flipped in favour of my opponent.