defiling the holiness of the Cathedral.
If ever this Cathedral had one like John Shelby Spong as a dean/rector or whatever the proper title, wouldn't his (or her) holding a leadership position and presumably teaching heresy or unbelief there be every bit as defiling? Or would this be... is the term Donatist? (Idea that the unworthiness of the minister/priest has no bearing on the effecting of a sacrament, but I don't know much about the Donatists historically.)
If, as an Orthodox, you (any Orthodox) believe that the Episcopal Church/Anglican Communion lacks any true sacramental grace by sole virtue of its not being in communion with the One Holy and Apostolic, why would you think that any act of non-traditional, not-grace-filled rituals performed in the National Cathedral is particularly defiling? Presumably that 'Cathedral' was never holy to begin with, yes?