Why do they need to pray at the cathedral? Washington has a major mosque; and doubtless many others.
Are they at the same time allowing a Christian service at the Washington mosque?
Is this a “switch of pulpits” for a day?
If not, why are they at the national cathedral?
... it may even be highly recommended depending on the nature of your visit and the circumstances. We know that the Caliph `Umar ibn Al-Khattab (may Allah be pleased with him), while in Jerusalem, was taken around in the ancient Church by the patriarch, but he refused to pray inside. When asked about it he said, "I am afraid, if I were to do so, Muslims might later claim it as a prayer place or a musalla.”