Operating system: Windows 10
Graphics card: GeForce GTX 970
Broken: All Blender versions including the latest 2.91
Short description of error
The mirror modifier doesn't do it's job properly when having "bisect" enabled. There is a hidden threshold to which it will snap vertices to the mirror line.
I ruled out all possible things, the mirror pivot is perfectly zeroed out and there is no merge enabled and also no auto merge. Stan from Blenderartists pointed out that switching to meters and scaling the object up 100 times “solves” the problem, so it's most likely a bug related to having switched the units to cm.
It's also not specific to the latest Blender version, it does the same error in older versions. I attached the scene so you can take a look at it.
Exact steps for others to reproduce the error
Load up the scene and simply put it to "bisect" and you will see how it merges the verts when it shouldn't.