I had a massive "Oh wow, yeah!" kind of moment recently, reading one of Bernard Lewis's books about the history of Islam. Lewis states that theatre was largely abandoned in the parts of the world of Classical Antiquity that answered the call to Islam. This was because the theatre was strongly associated with Greco-Roman Paganism and its tradition of morality plays, where actors would act out the myths, playing the roles of gods, demigods, and legendary human heroes — a practice rather offensive to Islamic values.
I used to do a lot of amateur acting, and indeed, thinking back on the decorative visual motifs of old theaters, and a number of subcultural quirks and traditions kept up in the world of theatre, there is an undeniable, but understated, Greco-Roman pagan vibe to it. Doing drama feels not unlike practicing a religion, in some regards.
I'm especially interested in symbology, and I wonder if any recent historian has done a systematic study of the many small ways Classical Paganism — or at least vestiges of it — live on in the Western world's institutions for theatre and the performing arts in general.
It seems that you're asking about Classicism (15th-18th centuries) and Neoclassicism (18th-20th centuries). Classicism is the emulation of extant Classical (i.e. ancient Greek and Roman) phenomena, while Neoclassicism is the aesthetic reflection of Classical ideals. Many theatre history textbooks discuss both Classicism and Neoclassicism in their respective periods. For example, Shakespeare's COMEDY OF ERRORS (1593) is highly influenced by Classical Roman comedy. But the play doesn't use the Classical world as much of a comment on current issues in 16th-century England, putting it in the vein of Classicism. By contrast, a play like Richard Brinsley Sheridan's SCHOOL FOR SCANDAL (1777) follows a strong Classical comic structure in its plot and characters but moralizes on contemporary English society, making it fit squarely with Neoclassicism.
But if you're looking for drama that directly engages with Greek and Roman paganism, you'll want to explore medieval Latin drama (which surprises a lot of people who still think of the Middle Ages as the "Dark Ages"). Check out Seven Medieval Latin Plays by Alison Goddard Elliott (New York: Garland Publishers, 1984).
Also, if you want to explore the topic of Islam and Greco-Roman pagan drama, see John Walbridge, "Explaining Away the Greek Gods in Islam," in the Journal of the History of Ideas Vol. 59, No. 3 (July, 1998): 389-403.