The colors are real but exaggerated during image processing by pushing color saturation much higher than normal.

I took a pic of the moon in 2018 and noticed the colors when playing around in Lightroom. At first I thought it was artifacts from my camera but after some research realized it was due to real Iron and Titanium oxides:

https://kevinloch.com/pics/color-supermoon-2018-01-31-0658z....

That's just a single hand-held shot with a Canon 5D Mark IV and 400mm lens, so it doesn't take much.

I don't know when this "mineral moon" style became popular but it's all the rage right now.