I understand Witsius's reasoning here but does this sound like one accommodating to the [Greek] culture?:
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Where is the appeal to the Greek custom of the day?
It is not Greek culture per se, but what the Greeks did when they worshipped. There was a certain decorum which was observed, and which gave expression to the proper distinction between men and women. To violate this decorum in Christian worship would only serve to bring shame on the participants. The same would be true in Judea, but the customs would be different; and the "angels" would have been present to observe the diverse customs of the Jews. The reference to angels is to the upholding of decency in the worship of God, but does not imply that the particular practice was itself unalterable.
For what it's worth, my wife and daughters wear hats, not because it is morally required, but because it is customary English dress for females.