This is assuming that the Byzantines do not seek reunion with Rome in an effort to stay alive, I would presume.
But the reaction would be something along the lines of official distance kept and unofficial relationships with the least radical of the Protestants (like the Lutherans, for example; keep in mind that Luther was very much troubled by the idea of Greek Christians being outside the communion of Christ according to standard German Catholic teaching of the time, and was one area in which the first cracks started to form in his Catholic outlook, even before his uninspiring trip to Rome).
As for the Anabaptists, Calvinists, and NonTrinitarians, I think the Byzantines would be outright hostile to them. It is not as if the Eastern Church did not have controversies and heresies of its own, after all. Doctrinal issues between west and east were not nearly as bad as liturgical and political issues, after all, and the Catholic line was probably the closest to the Greek Christian line as things stood.