The enemy of my enemy is my friend. The Crusaders happily fought alongside Greek schismatics(although, the schism was much more recent and less severe at the time, but it was still a schism nevertheless) in the first few Crusades. Refusing to cooperate at all with other Trad organisations because you don't agree with them on every minutiae, especially when said minutiae are not even relevant to the matter at hand, is just silly. You shouldn't sweep differences under the carpet, true, but you shouldn't let them get in the way of matters where those issues aren't even relevant, especially when you agree with each other on 99% of everything else.