I get the same issue as the OP.
I can use ALT-TAB whilst the game engine is loading up with no issues.
But when I am loading from the server list into the online official pve server of choice AND press ALT-TAB keys then the Conan Exiles client goes to a black screen, becomes unresponsive and never loads. I have to go to the task manager to close the client and restart the game again.
I’m not sure if this happens when I try to log into a single player game.
Once my character has loaded into the server then I can use ALT-TAB to go to desktop or other programs without any game crashes or lock-ups.
Honestly, I don’t know if they can fix this one. It might be that the process of loading the character to server gets priorities in a way that conflicts with alt-tab. Or it could do with our hardware set ups. So I’ve learnt to not alt-tab during the load to server (click - removes hands from keyboard and sits on them until loading complete - mutters to self “do not alt-tab, don’t just don’t, not yet”)