The mileage of the Activity loading pages correctly varies because the pane that loads it by default uses an older IE rendering engine. There’s a tool @TReKiE made that makes it so that Messenger uses the latest IE version when loading those pages (you have to restart Messenger afterwards if you already have it open):
Also note the Activity was originally made around 2005 for an official MSN Activity contest with a restricted browser frame in mind, and things on the web were done differently back then (JavaScript and fancy technologies were relied on less than they are now) so there was a greater amount of pages you could access through the Activity. Now that it’s 2020 and people rely on many HTML5 and JavaScript technologies for many sites functionality, that number has dipped quite a bit. Such is the way of the Internet, I suppose. 