I wonder if planes could be built in such a way to include two sheets of outside layer, with a gas (can a gas be used to shield radiation?) in between those sheets to shield the passengers from outside radiation.

Or maybe use a polyethylene layer?

The bulk of the radiation are cosmic rays or things showered from them. Shielding isn't practical.

But also, on the scale of things to worry about in life, this is way down there.

Cosmic radiation will penetrate anything that isn't, like, a good-size chunk of lead.