if R1C1 was Orange, then R2C2 would be Orange, and if R1C2 was green, then R2C1 would be green. You can't do that because orange and blue have to be in odd columns.
in R2C1 and R2C5 one is pink and the other is red. which is which corner is moot.
Right, I gave an example that was wrong in order to avoid spoilers, but the rules are still true.
R1C1 and R2C2 would be the same, just as R1C2 and R2C1 would be the same. <--- this is assuming the connected columns are 1 and 2, which I'm not saying is true because again, I'm not posting spoilers.
There's only one solution, so I'm surprised you're saying which corner pink and red belong in is moot. It's definitely not moot!