So was Francis I of France, nominally, despite his obvious rivalry with Charles of Habsburg. And yet, he still allied with the Turks.
Honestly, we shouldn't be overestimating the willingness of European countries to go on Crusade against the Ottomans when it goes against their interests and possibly leaves their flanks exposed for their enemies to attack. If anything, European political entities of the time would prefer to take advantage of the situation and react accordingly to Ottoman expansion, either allying with them or going into conflict with them depending on how events go. The Hussites would very likely become friends with the Ottomans in their struggle against the papacy and the HRE.
France is a bit different than the Teutonic Order. The main issue for the Latin world in this scenario is that all crusade and mutual defensive mechanisms are hampered by the divided state of the Papacy. This is why Bayezid himself felt it was a golden opportunity to make gains in the Latin world.