The Pope and Catholic hierarchy have a pretty high power level in 1400, enough for the Cinguettists to be uncomfortable about it. The Second Empire (though its more an Empire in name only) is still defender of the faith and has an intensely close relationship with the Pope, which extends to much of Western Christendom.
The Great Schism OTL was facilitated by more secular affairs, perhaps, than ours. Pope Sabinian II (#BattlePope) led the Western Christian armies to save Carthage’s bacon, not Constantinoples, and that made the Emperor pissed. This led to the relationship becoming more strained, until the Pope crowned the Over-King of the Franks Emperor in direct defiance of the Rhomanian Emperor.