What's the adjective for ecumenically? Here's the word you're looking for.
ecumenical
(ecclesiastical) Pertaining to the universal Church, representing the entire Christian world; interdenominational; sometimes by extension, interreligious. [from 16th c.]
“It won't be easy to go back to the authentic, though still imperfect, ecumenic spirit of reconciliation and communion, but ecumenism must go on.”
“The contributions of the Order have grown to the point that it is considered a major force in humanitarian activity The ecumenic activities have been recognised with the Pope John XXIII Award.”
“Its strength does not lie in the ecumenic compass of a single voice, in a lingua franca's paradoxically disenfranchising hold over the many.”