Your eyes have retinas, the things that let you interpret color. There’s rods, round things, and cones that stick out, which is what gives your eye a textured appearance in the colored part. The “cones” see color. The “rods” see shade, like black, white and grey. Cones only work when enough light passes through. So while I see the fabric as white, someone else may see it as blue because my cones aren’t responding to the dim lighting. My rods see it as a shade (white). There’s three cones, small, medium and large. They are blue sensitive, green sensitive, and red sensitive.
As for the black bit (which I see as gold), it’s called additive mixing. Blue, green and red are the main colors for additive mixing. This is where it gets really tricky. Subtractive mixing, such as with paint, means the more colors you add the murkier it gets until it’s black. ADDITIVE mixing, when you add the three colors eyes see best, red, green and blue, (not to be confused with primary colors red, blue and yellow) it makes pure white.

—Blue and Black: In conclusion, your retina’s cones are more high functioning, and this results in your eyes doing subtractive mixing.

—White and Gold: our eyes don’t work well in dim light so our retinas rods see white, and this makes them less light sensitive, causing additive mixing, (that of green and red), to make gold.

**** UPDATE to prove this theory I turned my phone brightness from the lowest to highest and saw it switching from white and gold (at the lowest) to light blue and darker gold (at the highest) meaning people that see blue and black are more sensitive to light (better eyesight and not looking at the sun like your moms told you)

but the lighting makes it look gold, so how would you know it's actually black unless you see the dress in normal lighting

it's an optical illusion

Hibiki says

by recognising there's a tint from the lighting

the tint makes the white look blue but how the hell do you see BLACK

by recognising there's a tint from the lighting