Q. Is it permitted to daven in a multi faith room in an airport?
A. Beis Avi (4: 31), Shevet Hakehosi (6: 83), Menuchas Emes (3: 6: n.24) rule not to pray in a multi-faith space, so is it amply quoted in the name of Rabbi J. D. Zoloveichik zt'l. (See also Remoh O.H. 94: 9, on davening in a non-Jewish hotel).
Horav Shlomo Miller's Shlit'a is similar, he suggests to daven outside of the non-denominational room.
Care should be taken as an array of diverse faith symbols may be exposed at the entrance of the room.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit'a