Spaniard Guardiola has until Monday to respond to the ruling body's charge that he displayed a political message.
"You can’t have and we don’t want football equipment to display political symbols. That has always been the case," Glenn told British media before referring to the recent controversy over British players wearing poppies on their kit.
"The problem we had with poppies is that for some reason a new person at FIFA seemed to think poppies were a political symbol and we fought hard against that notion and thankfully sense broke out," Glenn said.
"Things like a poppy are OK but things that are going to be highly divisive are not. And that could be strong religious symbols, it could be the Star of David, it could be the hammer and sickle, it could be a swastika, anything like Robert Mugabe on your shirt, these are the things we don’t want," he added.
"And to be honest and to be very clear, Pep Guardiola’s yellow ribbon is a political stance, it’s a symbol of Catalan independence."
Glenn said the FA was "even-handedly" trying to apply the laws of the game.
"Where do you draw the line? Should we have someone with a UKIP badge, someone with an ISIS badge?" he added.
(Reporting by Ed Osmond; Editing by Ian Ransom)
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