Can I ignore the neutral wire in a switch box?
For an ordinary single pole switch, it doesn't matter which brass screw gets which wire

A single-pole switch just opens and closes a circuit -- it has no sense of polarity or "line/load" requirements.  As a result, the two brass screws on a standard snap switch are interchangeable with each other.

The neutral is easy to handle

A dumb light switch has no use for the neutral, so you simply need cap off the existing neutral pigtail with a wirenut. 

P.S. your wires are in cables

What you see in the back of your box is a typical North American wiring practice in a house -- two two-wire-plus-ground NM cables entering the (plastic) box via built-in cable clamps that grip the cable sheathes, with one cable being fed from an always-hot power source and the other passing switched-hot off to the fixture, while neutral passes through the box without stopping.

Don't forget to attach the bare grounding pigtail to the green screw on the switch, by the way.