The reason why the emperor stands to the right of the empress is, at least at the enthronement ceremony, not because they are following the western style, but just because the emperor stands in the center while the empress is on his right from the viewer's perspective, meaning that they do not stand to the right or the left of each other.
天皇が皇后の右に立つ理由は、少なくとも即位の礼においては西洋に倣ったわけではなく、真中・向って右に並ぶのであって、左・右に並んでいるわけではない。