I'm curious to. I'm not finding any record of congress making any such designation (though record of politicians informally referring to it that way). Also not finding any reference at the cathedrals web site or the Protestant Episcopal Cathedral Foundation's (the organization originally chartered by Congress in 1893 to build one) to technical non-denominationalism. In fact it all seems to be very overt in its Episcopalianism and Christianiaty.
ETA: Here's the
full text of the original congressional charter.