The ground wires can touch, since they are both grounded. Keep the "live" wires apart.
For a while, I ran a 12-volt fan from two 6-volt batteries, one positive ground, one negative. I got 12 volts betwen the two "live " wires. And I kept the fan circuit isolated from any grounds. I also installed a 12-volt power outlet, and could plug 12-volt accessories, including a hand-held spotlight. But I had to wrap the spotlight shell, since it was grounded. Touch metal, and I would get a 6-volt spark.
(Later, I got a 6-volt fan, eliminated the 12-volt fan and second battery, and installed an inverter to provide 12 volts for garmins and cell phones.)