The thing with anime that have a premise that is completely out there (meteor fragments fall to Earth, every bear starts attacking and eating humans, humans build a big wall to keep the bears out, but then the bears disguise themselves as humans to enter their world, because a court allowed them to) is that after a few episodes, you start accepting the weirdness as the way things simply are in that world. You stop questioning why something is the way it is -- you start finding it quite normal that girls turn out to be bears ("Kuma shock!") and move on with your life.
The series is deeply symbolic, and it reminded me of Revolutionary Girl Utena. Utena has only yuri undertones, but this series lays it on quite thickly -- but that distracts from the real message. I haven't really worked out what that message is, exactly, but to me it seems like it has something to do with being your own person and not going mindlessly with the flow (which is what the Invisible Storm seems to be about).
The art is gorgeous (especially the backgrounds!) and I really like the fact that through flashbacks, you get to see the same scene from multiple viewpoints. That's a storytelling technique that works really well with anime because you can revisit certain scenes or occurrences and see them in the light of your increased understanding of the plot.
All in all, if you like weird psychological/deeply symbolic stories, or you like to see girls falling in love with girls (seriously, there are no males in the series, except for the three bear judges) then you should watch this.