Given: a video card with two video outputs (usually some version of NVidia) …. There is an application working with X11 using OpenGL, for example glxgears. You need to run two such applications at the start of the system (via .xsession), but independently on two monitors. I do not understand at all with the settings of video cards and X servers. Can anyone tell me how to split video outputs between two (?) X servers? Input from keyboards and "mice" is not so important … It is important that the video outputs of the card are independent for applications.
It's awfully difficult without special hardware and special software for this hardware. In any case, at that time (about a year ago, probably) my colleague was digging this question and telling me. The bottom line is the memory settings for the location of the displays inside the video card. This is called EDID and because of copyright it is only available in professional-grade cards like Quadro and FirePro. Maybe Wayland will do something like that (or have already done it), but on old systems everything is bad.