I got red wine out of white silk by using Natures Miracle. The original in the white spray bottle with red lettering. Spray on it and dab with paper towels

I’ve seen 50:50 hydrogen peroxide:baking soda mixes recommended for cleaning grout. Can you test in an inconspicuous spot first?

Grout does get stained faster if not sealed properly. As grout is porous, you need a penetrating cleaner for removing the wine stains through your grout. I found utmost satisfaction in this grout cleaner called Imperia. It is a deep penetrating formula that effectively removes all the deep-rooted stains and mold, revealing a sparkling surface. Homemade cleaners cannot give perfect results like grout cleaners. Although you get a clean surface after using grout cleaners, you cannot guarantee that staining will not occur again, and so it is important to seal the grout after cleaning.