I do not believe this can be explained by the facts surrounding the ban, but it can be (1) explained from scripture. The scriptural explanation can then be validated by (2) interesting facts surrounding the case.
(1) This is all about the doctrine of ’weak scruple’s and ’weak faith’ leading to the belief that the art of theater was unredeemable and worthy of a ban. This effectively attributes its practice as 'evil'. Just as banning Christian rap-music today would be attributing that form of music as unredeemable and literally 'evil'.
Although much more reasonably grounded, some ‘weak brothers’ back in the apostle's days also had ‘weak scruples’ and ‘weak faith’. 'Eating meats' 'sacrificed to idols' even when sold in the common market, seemed very horrible to them, because they could not shake their superstitions. They actually believed idols were real gods and 'evil.'. To this, Paul say's even though those who are stronger in their faith understand that this is not actually a sin (because there are no real gods) they must be careful in love not to offend their brother. They then need to think a bit before practicing their freedom in a way that might offend.
10For if anyone with a weak conscience sees you who have this knowledge eating in an idol’s temple, won’t he be emboldened to eat what has been sacrificed to idols? 11So this weak brother, for whom Christ died, is destroyed by your knowledge. (1 Corinthians 8:10-11)
In the end, Paul says you can still be free in your private life but not when others bring this question of conscience in your face:
27If some unbeliever invites you to a meal and you want to go, eat whatever is put before you without raising questions of conscience. 28But if anyone says to you, “This has been offered in sacrifice,” then do not eat it, both for the sake of the man who told you and for conscience’ sake b— 29the other man’s conscience, I mean, not yours. For why should my freedom be judged by another’s conscience? (1 Corinthians 10:27-29)
So the doctrine says that it is those of weak faith that assign material things to sin, whether it be drama, music, art, or even as horrible and 'sinful appearing' as food sacrificed to idols!
(2) In the case of the ban of theatre there is an interesting article (secular source) describing these events in detail called, THE CLOSURE OF THE THEATERS BY THE PURITANS.
The facts of the case show that on the 6th of September, 1642, the theaters were closed by ordinance. Then in 1656 they began to reopen. An interesting fact at the same time is one of the most influential Puritan writers, John Owen, was alive and preching in those very same years. He was a highly influential and an academic administrator at the University of Oxford and lived over the years 1616 to August 1683. In 1651, on October 24 he preached the thanksgiving sermon before parliament. This Puritan was very aware of the ban.
These surrounding facts lead to confirming the scriptural explanation, for Owen was a person who seems to have ‘great faith’. As evidence, in all the thousands of pages from his brilliant works, not once did he mentioned 'card playing', 'theatre', or any other similar past-time. He was so Christ focused that he could not be at all bothered, whatever his personal views may have been. I am referring to his published works, written by him.
So even at this time in 1642, when weak scrupled legalists were embarrassing the name of Christ, by banning theatre, and more pompously by promoting the 'upper class' entertainment of 'opera', strong believers were not bothered to even refer to the subject in their voluminous thoughts on a multitude of subjects. They may have avoided all such entertainments, so as not to offend their weaker brothers, but that only further manifest their maturity.
Regarding why 'theatre' was banned and not 'opera', it’s not difficult to imagine that 'sinners' would have enjoyed theatre more than opera. The language of theatre has always delveded more into sexual innuendo, etc. But in the end, not all plays could have been ‘filthy’. Opera would also seemed more proper as it would have appealed to the arrogance associated with the ‘upper class'. In conclusion, if Jesus would have come at that time this verse might have substituted the word 'tax collectors' with 'actors':
10While Jesus was having dinner at Matthew’s house, many tax collectors and “sinners” came and ate with him and his disciples. 11When the Pharisees saw this, they asked his disciples, “Why does your teacher eat with tax collectors and ‘sinners’?” (Mathew 9:10)