Not all of them were against acting. Apollinaris of Alexandria wrote Christian plays in the fourth century. The early Church historian Socrates Scholasticus says of him: “as a grammarian, [he]…paraphrased all the historical books of the Old Testament, putting them partly into [heroic poems], and partly reducing them to the form of dramatic tragedy. He purposely employed all kinds of verse, that no form of expression peculiar to the Greek language might be unknown or unheard of among Christians.” (source)
Other Church Fathers stressed the beauty and good to be found in Greek plays. So St. Jerome praises Sophocles’s play Oedipus Rex and says that in it there is “so great a display of wisdom.” (source) St. Clement of Alexandria shows his familiarity with another playwright, Euripides, saying, “Very beautifully, therefore, the tragic poet Euripides says in the Phœnissæ…[followed by a quote from the play].” (source)
Even the New Testament quotes from a Greek play – the phrase “Bad company ruins good morals,” found in 1 Corinthians 15:33, is pulled from Menander’s Thais, and is evidence that St. Paul read Greek drama. The plays of Ovid were used in Christian education for centuries, and found imitators, such as in the Plays of Roswitha, a nun from the 900s. (source)
St. Hildegard of Bingen, a doctor of the Church, almost single-handedly popularized the genre of “morality plays” through her drama “Ordo Virtutum.” During the counter-reformation, plays were part of the way that Catholic colleges instructed people and edified them – so you’ll find, in the 1500s, plays about Thomas More, Thomas Becket, and John Fisher, aka. Roffensis. St. Edmund Campion and St. John Paul 2 both were stage actors and playwrights. (St. Edmund’s Ambrosia appears to have influenced Shakespeare’s Macbeth.)
It is true that some of the Church Fathers wrote against plays, but these are often the writings of monks written as counsels to their fellow monks, who, as part of their seclusion from this world, were supposed to give up certain of its pleasures. Occasionally they highlight anything negative they can think of about the pleasures of this world – which are legitimate for laypeople – in order to discourage monks from reminiscing fondly about them, and when they call such lay pleasures sins, it is not always because they believed them inherently sinful, but because, for a monk who was committed not to enter the world again, to go to see a play went against a prior committment, and thus, for him, was a sin.
But plays themselves are not sinful, and our Church has a long history of supporting them in many ways.