Hi Long,
Your findings made me do a different test. I forgot the quotes around the variable in the view, but that does not make a difference. I now have this in the FacetWP listing, but it does not work:
[mbv name="display-related-things" vw_posttype="{{post:type}}"]
Passing the hardcoded value does work:
[mbv name="display-related-things" vw_posttype="activity"]
Somehow the value passed by FacetWP does contain the string "activity", but it fails to match in the if-statement. The hardcoded string works fine. Really weird.