So I've been playing with the new Gmail. We aren't alone - there are people posting in the Google forums and this causes eyestrain for more than just us.
What I did that gave me some immediate relief was pick a theme with a dark background (the chess pieces), and then switch the mail background to dark. This is the equivalent of "night" mode in Outlook or Android, and it helps a LOT. It's not a perfect answer, as I'm pretty sure that if I spent a ton of time in there it would still hurt, but it's much better.