4K monitor @ 60hz with late 2016 MBP
I didn't manage to solve the problem with the current setup. It seems like Apple still has some work to do regarding HDMI 2.0 @ 60hz. It simply doesn't work out of the box, at least not with this monitor.
For the sceptics:

Safe mode reveals the option to change the refresh rate, but still doesn't allow more than 30hz.
Resetting NVRAM and/or SMC did not help.
I tried using another monitor (same brand), another late 2016 MBP, another Apple USB-C to HDMI adapter and several different HDMI cables.

However:
Using a USB-C to Displayport cable immediately solved the problem. I used this one: https://store.google.com/product/usb_type_c_to_displayport_cable