I’m in the market for a new red dot sight, but have had some poor experiences with refraction in the past. In short, the few red dots I’ve tried (Vortex Spark AR, MRO, and one or two others) seem to have a bit of refractive shift, which makes my eyes/brain go haywire when shooting with both eyes open. My right eye sees the image through the sight, but based on what my left eye sees, it expects the image to be in a slightly different place, which gives me double vision and headaches. Things only get worse if the dot is not perfectly centered. The MRO I had was by far the worst I’ve tried in this regard. Even the tiniest shift off center caused double vision, so I returned it.
Are there any red dots that are better than others for sight picture refraction? I could buy another EOTech XPS, since I can look through those at any angle with no discernible refraction, but would prefer something a little lighter that I can leave on 24/7.

Regardless of what anyone says all red dot sights work best if you look through the center of the aiming window. They are more accurate and more repeatable when doing so.

Buy a quality RDS or get a scope. I have had excellent results with every red dot I have ever purchased, even the cheap made in China Primary Arms has worked well. I am not sure what your expectation is, maybe you have an astigmatism which interferes with aiming. In that case a RDS may not be for you.