I have astigmatism in one eye and not in the other. It's quantifiable also. On my prescription, the cylinder is "0.50" (and there is an axis that specifies the orientation of the astigmatism in 180 degrees).
Looking at a Trijicon slide-ride type mini-reflex, the 2.5 MOA dot is a starburst with either of my eyes. With the astigmatic eye, the burst is elongated vertically (the orientation of the astigmatism) so that it looks like a tiny octopus with legs hanging down. With lenses that correct the astigmatism, it looks like a round starburst.
0.5 cylinder is pretty mild astigmatism. More severe astigmatism will result in the dot looking like a streak, comma, football or some other less symmetrical shape.
With no astigmatism, I would not expect to see a circular disc with crisp edges in a mini reflex sight. This has to do with how close the diode (LED) is to the reflecting surface and how that surface has to be curved to reflect the diode so that it is focused at infinity.
The best way I've been able to tame the starburst is to turn the brightness down. If I dial it down two steps from the auto-adjust level, the dot bursts much less. The auto level is set to make the dot easy to find. The brightness can be adjusted manually and locked in, but I use the auto level for my carry optic so that it will be easy to find under various conditions. If I set it down two-levels manually, I can hit anything within 2.5 MOA so long as I am able to hold it steady or rest it.
If I use the factory adjustable rear sight and front ramp, I can use a particular tiny spot on the front sight to make small groups -- the gun's precision is there -- but I cannot be as accurate as with the reflex sight.
I tried to simulate worse astigmatism. First, I tried doubling-up my corrective lenses, but that didn't seem to work. Instead, because my astigmatism is vertically-oriented, I tried turning my corrective lens 90 degrees. I also tried looking through the correcting lens with the non-astigmatic eye. The results were disturbing to the image, but not so severely that the reflex sight would be unusable. I could only speculate that at some point beyond a 1.0 cylinder, I would begin to consider an alternative to reflex sights. I think if I had 2.0 cylinder in my dominant eye, I could still use reflex sights with corrective lenses, but I would have to consider that I might not have or be able to keep my corrective lenses on in some circumstances. While that would not disable my use of the sight at short ranges, it would diminish or eliminate any advantage gained from the reflex vs. standard sights.