Blue moon refers to when there are two full moons in one month, and not to the color of the moon. When we look at the visible moon what we see is reflected daylight. When taking a photo of the moon with a digital camera, to get a natural color we would use the Auto or Daylight white balance setting on the camera. Indoor tungsten or incandescent lighting is orangish in color, and when the white balance is set to incandescent, the camera will add blue to offset the orange, because orange is very close to being a complementary color to blue as you can see by the color wheel image.
Image of the blue super moon where I changed the white balance before taking the photo, only post processing was cropping/resizing.
Color wheel showing primary, secondary, and complementary colors, tertiary colors are not shown
Super moon with dissipating jet contrail, white balance set to daylight.