I'd think the Trebizuntines would encourage conversions by making Muslims second or third class citizens, forced movement to different parts of their empire when rebellions occur and I'd think a lot of children would truly be orthodox Christian even if their parents aren't. Another interesting thing is syncretism between coptic Christianity, Orthodox and Islam. Would those religions be successful and be accepted as Orthodoxy?I suspect a lot of them would conveniently pretend they were Christians all along. Most of them converted to Islam out of a desire for personal advancement instead of truly believing in it, so the reverse is also possible. Unless of course the Trepezuntines have the ability to disseminate the Muslims Greeks and Greek Christians and just adopt a policy of kill 'em all.