Can rework Galio E pass through non-terrain walls?

No. Galio's new E ability (Justice Punch) is explicitly designed to be unable to travel through walls. This is because Galio is meant to be an initiation-style tank character - running away is counter to his theme.

From the official reveal:

Galio hops back to wind up for an epic haymaker. After a brief delay, he charges forward, dealing magic damage to enemies and knocking them up. Galio's charge stops upon colliding with a champion or terrain.

Since player-created terrain such as an Anivia wall or Trundle pillar does count as terrain, Galio should be unable to pass through it.

You can see the punch in action, as well as its interaction with terrain, in the official champion spotlight on Youtube.

No. From the rework page:

E: Justice Punch
Galio hops back to wind up for an epic haymaker. After a brief delay, he charges forward, dealing magic damage to enemies and knocking them up. Galio's charge stops upon colliding with a champion or terrain.

I also happen to have PBE access right now, and I can confirm that this is how it works, having seen plenty of people playing Galio.