You can't join servers which don't have the mod so you probably have to restart mc with and without the mod all the time.
It says:
Connection lost
Incomplete set of tags received from the server.
Please contact server operator.

Identity is required on the client and server. Just like many other mods that add content, you will have to disable the mod to join a vanilla server. The tag issue is a game limitation and outside my control.

To separate your game profiles and avoid having to switch out mods when you visit different servers, I would recommend using MultiMC.