I had that too. Dodging behind a wall inside a building, full shield and still got hit through it...
...while the plasma gun of the alien destroyed the wall.
Destroyable cover is something you have to keep an eye on now. Works well the other way around too tho.
Since there is no point in going slow or silent after concealment is lifted, I use 2 grenadiers to make the enemies cover go boom.
Blowing shit up looks great, is fun and very useful. But now that you mentioned the full shield destroyable wall cover, I actually understand your frustration.
Just wait till Mutons throw grenades around, those bastards!
Oh, and as clarification: full cover means you get a low hit chance, not a 0% hit chance. Also, the damage you take in full cover is lower than normal and the crit chance is lower too.
It doesn't not mean you're invulnerable behind it.