Hmm indeed weird - I thiiiiink (not 100%) that their GetCapabilities is wrong. FME gets redirected to a different url which is defined in there as the GetMap request url. If you look in your FME log with just a basic reader you end up with a GetMap request URL which looks like:
http://geodata.naturvardsverket.se/arcgis/services/planeringsunderlag_o_strategier/MapServer/WmsServer?....
But the URL you've been provided is:
https://geodata.naturvardsverket.se/planeringsunderlag_o_strategier/wms?
If you replace the URL back to the one you provided (in a browser) then you get a result:
My guess is that the GetCapabilities document is wrong and needs to be fixed, but I'm not 100%. Likely QGIS is not using the URL provided in the GetCapabilites document but the one provided.
I suspect that the people who set up the service didn't spot the issue because it's an internal URL and it probably works for them.
I'm not sure if there is a workaround for this.
Thanks! That answer taught me a bit or two about WMS Hm, for now I might end up downloading their raster file instead then.