Hi Kenny, simply said, for most common dishware, yes, the green side is safe. But as with anything you will have to define common. Not knowing the plastic dishware you could be using, it may or may not create scratches. Ceramic dishes, although not unheard of, will probably not scratch.
The whole intent of washing dishes is to remove food residue that would ruin the taste and look of the next food served in/on it, and that can grow bacteria. Proper washing with soap and clean rinsing with water will get rid of that residue which could harbour bacteria.
Green side is to help remove stuck on residue. Yellow side is to hold and make the soap sudsy which helps lift and remove the residue you have loosened with the green side.
So if there are scratches created, whether or not by the sponge or any other agent or tool, the act of using soap and water is the purpose and reason for washing them, to get rid of whatever is left on them.
All of the above preferably done with the hottest water your hands can tolerate.