Rubbish, you haven't looked at the OP's actual circuit, all the LEDs can be on at once if he uses the resistors in his own schematic.
Take it easy there Grumpy. I've seen the circuit. You can't assume anything is correct. This is the datasheet of your typical rgb led.
Typical current is 20 mA. Typical voltage drop is 2.0V for red and 3.2V for green and blue.
And if you had looked at the MCP23017 datasheet you would have seen absolute maximum source current is 125 mA while sink current is 150 mA. In general, circuits can sink more current than they can source. That's why it's better to use common anode leds.
No rubbish here. The OP wanted to use a 330 ohm resistor. According to the datasheet 90 ohms is in order. Unless it's a very dark room, the leds won't be visible.