I've seen pics of HRH as Gold Stick in Waiting riding astride in white breeches and thigh boots - which would not be appropriate for inside the Abbey I think. Imagine the noise she would make walking down the aisle!
Also seen a pic of her, standing, in trousers and ordinary shoes presumably, which would look much better inside the Abbey.
Riding sidesaddle ["astride" edited out] is very unlikely for the Princess Royal but we never know. She could surprise us but I think the long skirt is not suited to walking because it is a strange shape. Not sure.