The MIDI Breakout Board is specified to work with 3.3 V. However, in that case, it outputs only about 3 mA, while MIDI requires at least 5 mA. The MIDI Electrical Specification is quite clear that much smaller current limiting resistors would be needed.
(3 mA will work with this board’s input, but many MIDI devices use the 6N137, which actually requires 5 mA.)
As for the input: the 6N138 requires a decoupling capacitor; and its guaranteed bandwidth is too low for MIDI unless you decrease the output transistor’s Miller effect by adding a resistor to discharge its base: