If there is any conflict within the Alliance it would not be started by Varian.
The way they have written him in the games and novels is that he is the anti - Garrosh. He starts of rash and full of rage and completely unreasonable and they had him go through all this soul searching (contrived as it may be) that he now mostly keeps his cool and is a lot more willing to talk things over.
So yeah the best bet for Alliance tension was back in WotLK where he was still all for the extermination of all Horde races whilst other more diplomatic leaders like Velen or Jaina(yeah yeah Blizz oh the irony) might have been at more odds about that.