The law involved is from the Roman period and was essentially about protecting the integrity of the privileged social classes. So it's not that nobody could marry an actress, just not men of a high social class. Why the prejudice against actresses? Actresses, as has been the case at some other times too, were often also prostitutes. See here. That made them, in the opinion of the law until Emperor Justinian changed it to allow for his marriage to a former actress, unfit for marriage to men of high social standing.

In early Byzantine society, women whose occupation was related to public spectacles and entertainments such as dancing and singing were prostitutes. See chapter 3 of Constantinou, Female Corporeal Performances and Leontsini, Die Prostitution im frühen Byzanz