It still reproes with factory settings. I don't see anything related in the output of blender --debug-all --verbose.
It actually seems to be the case with any context window shown in the main viewport (e.g. W -> Subdivide -> Right Click -> Online Manual does nothing).
I can open the online manual in other places, e.g. Object Properties -> Location X -> Right Click -> Online Manual opens up https://docs.blender.org/manual/en/2.91/scene_layout/object/properties/transforms.html#bpy-types-object-location in my browser.

Thanks Jean! Applying the mirror modifier before limiting does seem to work.

I can still repro on:

Hit another one, this reproes pretty regularly

This is the output:

So I can't create this from scratch with factory settings, but if you open the file from https://developer.blender.org/T73174#851823 with --factory-startup, then enable the godot exporter and repeatedly export, blender will eventually crash.

I've disabled all addons but the exporter and can still repro.

There's something about my preferences causing this. If I use blender --factory-startup, I can't repro it. With --factory-startup, I don't see that gray frame after selecting the parent. It seems that blender stays in edit mode with the mesh selected, regardless of whether I select the parent or child.

Sorry, this is a tricky one to repro, and it doesn't seem to be 100%.

I've managed to find a reliable repro. Let me know if I should continue the discussion here, or on godot-blender-exporter, or both.
I normally report bugs in the exporter only to the exporter (as @Julien DUROURE (julien) mentioned), but I figured anything that manages to completely crash blender might be of interest to the blender devs.
For the repro: