Hi Pelle
Is it a specific layer from the service you have issues requesting?
I just tried accessing the service using this URL:
https://arealinformation.miljoeportal.dk/gis/services/DAIdb/MapServer/WFSServer?service=WFS
Notice that I have removed the Request parameter (request=GetCapabilities&) from the URL as MapInfo Pro adds this itself and sometimes including this parameter gives some weird results.
I did successfully download the layer Fredede_Omr.
I guess you are aware that there is a list of services from Danmarks Miljæportal listed here: https://danmarksmiljoeportal.zendesk.com/hc/da/articles/360000230869-Arealinformation-Webservices-2018
I also tested that it works if you apply a Bounding Box filter and it does.