Well, after having a nap I thought about what could go wrong and it seems like I was right.
I don’t use the ready to go 802.3af PoE module because I have an existing ethernet cable for a TP-Link router which is powered by 24V passive PoE which is not 802.3af. As the pinouts for PoE are quite easy to use on the AR150 I wanted to attach my own PoE solution for that 24V passive link. However that failed as described before because I did not get a link if I attach the cable having 24v passive PoE.
Now I know why: The connection failed because even though the TP-Link passive PoE injector is 10/100mbit only, the switch I use fails to negotiate a connection if I don’t manually enforce 100 mbit full duplex. Works fine on the TP-Link CPE210 though without it. After enforcing the link speed on the switch everything works fine. Will keep you updated and put a report here how to power it through passive PoE as this was requested a couple of times before 
Long story short - If you try to do your own passive PoE solution on the AR150 and have a gigabit switch, make sure to set that link to 100mbit FDX fixed otherwise it may fail.