I found a workaround (but it will only work on windows).
Start git daemon with verbose from cmd.exe:
"C:\Program Files\Git\bin\sh.exe" --login -i -c 'git.exe daemon --verbose '
Not tested, if it works directly in git bash. Maybe it will.
Then (before starting any clone, pull, fetch,...) select some text in the window (note: "Quick Edit Mode" must be enabled (can be found in: cmd.exe --> Properties (click the top left corner of your cmd window) --> Edit Options)) in which git daemon runs. That will prevent it from printing any further messages in that window.
When the output thread of git daemon is blocked that way, then the error does not happen