Every special move can be done as a wakeup attack(plus backdash and throw). Most wakeup attacks gain no invincibility but some do, anywhere around 1-3 per character. The invincibility varies. Some moves are fully invincible and some only have limited invincibility, so they can be stuffed. For some moves the invincibility is gone early into the move and it's easy to stuff, sometimes it's only a few frames and it's very difficult.
The timing of when you do the wakeup attack during the knockdown can throw off the opponent's attempt to stuff it. For example, if you input the wakeup late it may still have invincibility when your opponent is trying to stuff it to beat a fast input wakeup attack.
You can delay wakeup by holding flip stance. There is a short and long delay depending on how it is held. If you delay wakeup you disable the ability to do a wakeup attack.
Pro tips:
I've seen a few wakeup attacks complained about as being too good or free that are not actually fully invincible and could be stuffed. This will be a key skill to learn and you can expect the super top players to have mastered this while others don't get it. So if you want to make some of that e-sports money I'd spend a lot of time on this.
On the flip side, by mixing up your timing and throwing in the delayed wakeup you can throw off someone who's good at stuffing these semi invincible wakeups. So don't flip out and assume you literally can never wakeup if your character lacks a fully invincible wakeup attack.