What is this red powder under my carpets?
I am just viewing a picture but I have pulled up carpet pads on concrete in many a house and it looks like caulked adhesive used to secure the pads to concrete.  Sometimes the colors in the pads bleed into the adhesive (the spots in my house were green) and things definitely break down or turn to powder after a while.  You should be able to scrape it up - wear some gloves and a mask if you are worried.  I will say I had way more green powder on my floor than that.