This is a common concern in our world, too. I hear from people “I would come to services, but it’s ‘casual Friday!’” (of course, here in Portland, it’s always “casual Friday!”). Guests, who come to services for the first time are concerned about what to wear.
Maybe it depends not on what’s happening inside the synagogue, but what’s happening outside:
R. Ashi said: I saw R. Kahana, when there was trouble in the world, removing his cloak, clasp his hands, and pray, saying, ‘[I pray] like a slave before his master.’
When there was peace, he would put it on, cover and enfold himself and pray, quoting, ‘Prepare to meet thy God, O Israel.’ (Amos 4:12)
Or maybe, its less about what one wears on the outside when praying than what one prays on the inside while wearing.