Hi @Andrew302958 and welcome to the forum, we are happy to have you here.
You are correct, the active cooler and the PoE M.2 HAT+ are incompatible. The Active Cooler takes up too much space on the Pi5 to accept the HAT without extra long headers.
If you really want maximum cooling (say, heavy M.2 + PoE workloads), you can skip the Active Cooler and instead use a third-party case with a larger external fan, or mount a blower fan that pulls air across both the Pi and the HAT. Some community cases already exist for this.
The following product works with an active cooler. I have one on a Pi 5.
I wanted POE as well as an M.2 full length adaptor. Never had a problem with any Geekworm products.