The M&P Shield is a down-sized version of its larger M&P brothers. However, while the compact versions are literally just smaller copies of the full size M&Ps, the Shield has some unique differences. One of those differences is how the thumb safety works.
I've always stated that the thumb safety on M&P pistols is superfluous. I haven't changed my opinion even when talking about the Shield. Sure it has some value, I just don't think it's much. Still, it exists and does do a good job of blocking trigger movement. Here's how the Shield works:
This is with the thumb safety on...
Here the thumb safety is off...
As you can see in these two pics, the thumb safety has a tab that blocks the trigger bar from moving. That tab contacts the trigger bar extension here:
On the full size guns it blocks the trigger bar at the bend just prior to the trigger bar loop like this:
In essence both thumb safeties work the same; they block trigger movement. There just isn't room in the thinner Shield to use that same bend effectively. It doesn't explain why S&W chose to make it single sided. They could have made it ambidextrous like its larger brothers. That would have been more in line with the original concept.
In the end it doesn't matter. As a lefty I just don't use it. The gun is every bit as safe with or without the thumb safety. It won't fire unless the trigger is held back. As long as you keep your finger, and other objects, out of the trigger guard, the gun is safe.