I have replaced my electrical garage door opener. New model is Chamberlain ML750. Original opener had what looks like a doorbell mounted on the wall to open/close the door. New opener does have some connectors for a wall mounted switch to be connected. The manual refers to white & red wire but my old wire is green and yellow. Am I right in thinking that, as this is just a simple switch, it shouldn't matter which way round I connect the wire?

So long as it is just a 2 wire connection I would say your safe. What it seems to be doing is connecting one side to the other to make a circuit through the switch.

You should be fine.

Lots of times they used thermostat wires with 4-6 wires. Any 2 should work

Correct, color of insulation does not matter. To avoid confusion, I would color each end of one wire, say yellow, with a red marker. Color the other wire,(each end), with white.