Beaglebone Black ROV Control Scheme
Several things to comment here.

First off, if the joystick puts out 3.3v then it won't damage the BBB. If you can control the wiring of the joysticks (I'm assuming they're just microswitches and you can modify the wiring), then a better plan would be to connect a ground signal to one side of the j/s switch and the BB to the other. Atmel chips have built-in pullups. I can't imagine the BBB has that feature. In which case, connect the signal to Vcc via a 10K or 47K resistor. Add a small capacitor for debounce.

In normal operation, the switch is open. The resistor pulls your signal input to a high state. When you operate the switch, the resistor gets shorted to ground and your input goes low. The capacitor just takes the "edge" off the signal to avoid the rough edges you get with your average switch.

I'd second someone else's comment about using relays. Your bilge pumps operate on +12v with a current of around 2A (give or take). You can use an N-channel MOSFET to drive the pump instead. Connect the + to +12v, and the - to the drain of the MOSFET. Connect the source to ground and the gate to the BBB. Cheaper, smaller and better than a relay. Also put a shunt diode across it.

Make sure to use a MOSFET which has a gate threshold compatible with the BBB output or it won't switch on.

The other advantage of the MOSFET is you can pulse the stepper quite quickly.  To avoid the pumps "kicking" when turned on, you would switch them on in software for a millisecond (for example), then leave them off for 9ms.  Turn them on for 2 and off for 8, etc, until they're fully on. That way, as you operate the joystick, the motors will rev up, rather than kicking hard over and making small movements difficult if not impossible.