they update after a left click
happens even when force crosshair updates is on

Pushing out 1.2.1 to fix this as this affects anyone with the default settings.

Was just encountering this same issue and switched around mods until I found out it was Exordium. To add more info to this bug:
The crosshair doesn't invert, disappear during F5 or spectator, can't be forced to update, does this even with "Fast Crosshair" set to OFF, and it doesn't seem to be a mod conflict of any kind.

For me the crosshair updates when punching, however it stays in the hidden mode when switching back to first person which is annoying. You have to punch again to see the crosshair again

Also the option for fast crosshair doesn't toggle the crosshair, I think its always enabled by default

Huh that's an odd one, since the crosshair should not be touched at all as long as the buffering is off. Will look into it.

private BufferedComponent crosshairBufferedComponent = new BufferedComponent(true, () -> ExordiumModBase.instance.config.debugScreenSettings)

Ah damn, you're right. That copy-paste fail made it through.