Two things to keep in mind about Gosson. One, he’d written stage-plays himself—he speaks of Catiline's Conspiracies as a "Pig of mine own Sowe”—and had recoiled in horror. Two, he loved trash-talking the gods. “Iuno crieth out in Seneca ... Let’s dwel in earth, for heauen is full of whores.” And “Apollo is a buggerer.”
Stephen Gosson makes no complaint of Athena in The School of Abuse (1579), saying only that Maximus Tyrius "attributeth the beginning of vertue to Minerva."
But this passage, from Playes confuted in fiue actions (1582), appears to be what Waugh has in mind:
“If their Gods be to be honoured, but theire Gods are by no meanes to be honoured, therefore theire playes are by no meanes to be receyued. [De spectaculis] Tertullian teacheth vs that euery part of the preparation of playes, was dedicated to some heathen god, or goddesse, as the house, stage, apparrell, to Venus; the musike, to Apollo; the penning, to Minerua, and the Muses; the pronuntiacion and acton to Mercurie: he calleth the Theater Sacrarium Veneris, Venus chappell, by resorting to which we worshippe her."
Waugh has carefully not quoted this relevant bit from Gosson: “Tertullian affirmeth yt Playes were consecrated vnto Bacchus."
Clearly Stubbs has plagiarized Gosson, almost word for word. And in turn, Gosson has warped the early Christian moralist Tertullian, who writes:
"At first the theatre was properly a temple of Venus. ... But Venus and Bacchus are close allies. These two evil spirits are in sworn confederacy with each other, as the patrons of drunkenness and lust. So the theatre of Venus is as well the house of Bacchus: for they properly gave the name of Liberalia also to other theatrical amusements—which besides being consecrated to Bacchus (as were the Dionysia of the Greeks), were instituted by him; and, without doubt, the performances of the theatre have the common patronage of these two deities. That immodesty of gesture and attire which so specially and peculiarly characterizes the stage are consecrated to them—the one deity wanton by her sex, the other by his drapery; while its services of voice, and song, and lute, and pipe, belong to Apollos, and Muses, and Minervas, and Mercuries."
Venus and Bacchus are blazingly the leads in this company; the rest of the pantheon is "also appearing." They're not even named as individual deities, but dismissively as types: "Apollines et Musas et Minervas et Mercurios." Tertullian is so hostile to the pagan gods that he lumps them together as "Apollos, and Muses, and Minervas, and Mercuries." And so forth, and so forth. They're certainly not assigned individual roles. He just treats them all as gangs of devils.
You will note that writing isn't mentioned. Hardly surprising, as Tertullian's real target is the Roman Games: the circus, the gladiatorial combats. What he loathes is spectacle.
So Gosson has to translate Tertullian's attack on an alien recreation into terms related to Elizabethan playhouses: not known for blood sacrifice or dazzling spectacle. Gosson has tried hard to rationalize that passage; he’s tried to attach an action to each god. But Minerva has no mythological connection to the theatre at all: her oversights are the strategy of war, wisdom, weaving. She's there in Tertullian simply as a abomination for Christians to shudder at. Gosson has to invent something for her to do, and “penning” is the closest he can come. (Of course, "penning" is what he himself did in his brief association with the theatre, so he may well have a particular aversion to it.) The Muses, of course, include Thalia and Melpomene (Comedy and Tragedy), so he clumps her with them. In short, when he tells us that "euery part of the preparation of playes, was dedicated to some ... god, or goddesse," he's confabulating. Making stuff up.
In this tract, Gosson is explicitly replying to Thomas Lodge's A Defense of Poetry (1579). Lodge had just pwned him:
"But tell mee truth, Gosson, speakest thou as thou thinkest? what coulers findest thou in a Poete not to be admitted? are his speeches vnperfect? sauor they of inscience? I think, if thou hast any shame, thou canst not but like and approue them: are their gods displesant vnto thee? doth Saturne in his maiesty moue thee? doth Iuno with her riches displease thee? doth Minerua with her weapon discomfort thee? doth Apollo with his harping harme thee?—thou mayst say nothing les then harme thee, because they are not, and, I thinke so to, because thou knowest them not."
"Thou knowest them not." Why on earth would the allegedly well-educated Oxford take a name from an error propagated by a frothing fool?
In short, the only early modern writers who in any way attach Athena/Minerva to any aspect of the theatre are Stubbs slavishly copying Gosson misreading Tertullian who hated all the gods.