X2Go Client should be able to run under any and every X11-based desktop environment. Wayland-based desktop environments need testing.
X2Go's “X Server” is called “nxagent”. It is part of the nx-libs package.
As of version 3.5.0.x, nxagent is forked from the X.org 6.9 codebase (from 2005.) Therefore, there are 4 reasons why certain modern “3d-ish” desktops are incompatible with nxagent, and therefore X2Go.
Ultimately, addressing issues #1 and #2 requires a lot of work. Solutions are discussed here.
It is recommended to switch to using a compatible desktop environment if your desktop environment is listed below as incompatible.
In X2Go Client, you must specify the Session Type as: Custom Desktop: icewm-session
In X2Go Client, You must specify the Session Type as: Custom Desktop: openbox-session
Compatibility issues with Cinnamon are being tracked in bug 150
In X2Go Client, You must specify the Session Type as: Custom Desktop: /usr/bin/enlightenment_start
However, bug 555 (Windows cannot be moved by dragging) was encountered, and not much testing has been done.