Ok this is very weird… First I found out that I had to install the „bugfix for shairtunes2“ in Max2play. I installed it and so the Shairtunes2 plugin loaded correctly in LMS. It still does not work with Allconnect (it seems to play correctly but no sound comes out). But now it works with MediaMonkey!
However I am not sure if music is cast from my phone or if it plays from the external hard drive connected to the Raspberry Pi as they have identical libraries. But at least it works for now.