I noticed the same thing when I captured a Muslim missionary... it's an odd feature to let you capture a unit that you really can't use... and it isn't obvious that he's still Muslim; I can see a lot of players accidentally trying to use him and not realize they're spreading someone else's religion.
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Yes- the only way I know to check is have the missionary beside the city and mouse over the convert button. It would be helpful if is said "Catholic Missionary" or whatever.