I purchased a CORE about 6-7 weeks ago. When loading a magazine, fully loaded, with the slide open, if I insert it semi fast/hard, the slide will close on its own. It loads a round and is ready to fire. I have to consciously load it softly to keep it from closing. Then of course, I can sling shot the slide as normal.

I bought the gun new, I did not shoot the gun stock. I ordered an apex trigger kit and installed it before I ever loaded and shot the gun. So I am not sure if it is maybe something I did or if it's just a flaw in the gun. I have installed apex kits on 2 other M&P Shields. I am not a fan of the M&P trigger, so I didn't even bother with the CORE stock set up.

Anyone else's pistols do this?

Yes, others' pistols do this.

There are many long threads on this issue, sometimes referred to as auto-forwarding.

It is easily controlled by adjusting the friction point between the slide stop and the slide.

I make sure all my semi-autos will do this for faster reloads. Having to manually close the slide with extra time, movement and manipulation doesn't make sense to me when simply inserting the mag forcefully, which I want to do anyway, will close the slide and chamber a round.

Others don't like it and think it is a problem. Run your pistol the way you are comfortable, but explore options that may actually be beneficial. Don't like it? Rough up the slide/stop interface with a file or 400 grit wet/dry sandpaper, or send it back to S&W and they will do it for you under warranty.

If the Users Manual is the same for the C.O.R.E. as the regular M&P's, page 17 address's it.
"WARNING: DO NOT USE EXCESSIVE UPWARD FORCE
WHEN INSERTING A LOADED MAGAZINE INTO THE
PISTOL. EXCESSIVE UPWARD FORCE COULD CAUSE
THE SLIDE TO MOVE FORWARD, CHAMBERING A ROUND
AND MAKING THE PISTOL READY TO FIRE."

Good to know. Thanks.