I think the main reason to destroy Shaylia's reputation has to do with the heroine being a bastard baby? I mean, yeah she was born from the (ILLEGAL/TABOO) romance from the saintess and the crazy emperor. If she had been legitimized, she would have been in line, but I don't see that happening if she had stayed. Balancing that, she is strong in the goddess's features (gold eyes, red hair) which are implied to be part of the local religion and cultural importance, whereas the current imperial family lacks them, which added to the fact that they are the line of the younger brother (that may have had to usurp his crazy brother) and the whole line may be considered out of the goddess's favor in some circles.
Even now, Shaylia's brother has been named heir, even though she was born first, and is legitimate, and therefore has a strong argument for getting the crown as well. I bet there is an issue between the church and the current Imperial family / Shaylia's faction in some way.