I play a multiplayer game via LAN, hosting a saved game. When someone joins the game, they are instantly desynced, after installing and activating the toolbars mod. One thing I noticed - when auto-pause while joining is activated, normally all windows are frozen in place and any click is disabled. The toolbars ignore this behavior. Maybe that's a problem?

Desync report: https://we.tl/t-yUmpJfvGSw

I see a lot of mods installed. Can you verify it only with toolbars-mod? I've never played multiplayer and never received any report of desync from users. Also has no clue what can cause desyncs and how CRC is calculated, documentation about desync is almost non-existing.

Okay, toolbars mod only in vanilla space age works fine in a new game. This lead me to test it with all my mods activated again on a new game with the exact same map exchange string from the save that causes the desync. That works fine too. So it shouldn't be an interaction with other mods. Toolbars was added later to an existing save, can this be a problem?

Frankly saying have no clue. As mentioned before there is no comprehensive description of what can cause desyncs and how to analyze it.
There is a thread on the forum about desyncs. Maybe wube could help in identifying the problem.
https://forums.factorio.com/viewforum.php?f=209

Okay, it works when I set auto_pause_when_players_connect to false. Then I get no desync. So I think the mod is ignoring this autopause and does things which lead to a desync then.