Minecraft 1.10.2, Minecraft 16w33a, Minecraft 16w35a, Minecraft 16w36a
Structure blocks are intended to be indestructible just like bedrock and command blocks. However, I've found that wither bosses are able to break all the types of structure blocks both when they are damaged and with their blue skull projectiles similar to the resolved issue of withers breaking barriers (
You can reproduce this by spawning a wither inside a box of structure blocks and damaging it or waiting for it to shoot a blue skull.
In some rare cases as well, I noticed that structure blocks adjacent to the ones that had just been broken appear to change texture. I'm not sure if this is a related bug but it caught my eye as I was testing this.
This is a somewhat annoying bug for mapmakers and other purposes so I would greatly appreciate it if it was fixed.