I did the first chapter of the Kyrian campaign today. It's quite good, but also kind of weird.
Basically you're following one of the Aspirants around as she prepares for ascension. The two of you go to Azeroth to escort a soul back to the Shadowlands. In Azeroth, you meet the soul of Ben Howell and relive his last day.
It's a pretty cool quest, one where you're just a good, average man with a family. I won't spoil how he dies, but it was pretty touching and tied in with the original story back in Azeroth. However, once you finish that part, you escort the Ben's soul back to Oribos where he is promptly thrown into the Maw!
It kind of illustrates how wrong the Kyrian are. If the Forsworn were a pure third-party faction, then it would be very tempting to join them. But instead they're allied with the obvious bad guy, which just makes them seem stupid as well.
I guess we'll see how Blizzard resolves this in future chapters, but so far I think the execution of the Kyrian parts of the story have been pretty poor, and greatly hurt the faction.