There's many example of FF characters being able to use both types of magic.
But Eorzea seems to be a universe where using both of them seems far less possible than in other FF games which treat Black Magic as being simply elemental magic rather than demonic as this game suggests it is.
In this game, each one seems to represent two contradicting faiths. One is warm, giving, healing, and calls upon nature, while the other is destructive, corrupting, demonic, and calls upon the Void. Going by the storylines, it seems like it would be very difficult for a sane-minded individual to be balanced and masterful of both schools to the point of being able to unlock the Soul Crystals.
But it was mentioned at one point that Red Mage MIGHT be unlocked through having both a White and Black Mage...
Can anyone enlighten me?