From what I understand, the dyes used in dark colors tend to be less transparent to the wavelength of UV light, and thus absorb some of the UV instead of letting it through. As a side effect, that also makes them heat up more, but the skin is technically more protected (assuming a like-for-like garment, as it’s likely that a thick white shirt will still be more protective than a thin black one).

Looking into it again for this comment, it appear that all color dyes offer some UV protective effect in clothing, and the more intense the color, the more protective it can be (though still varies by the specific color itself). There’s a more in-depth explanation of how that works in this scientific article, under section 6.6.2. I’ll put in an spoiler for convenience sake.

:::spoiler How Dye blocks UV The UVR protecting ability of the dye sources depends upon absorption characteristics of the functional group present in the chemical structure. Sankaran et al. reported that the UVR protection ability of cotton fabrics was effectively improved when dyed with vegetable and animal dyes from madder, indigo and cochineal [79]. Some direct, reactive and vat dyes with darker shade are capable of giving a UPF of greater than 50 due to the nature of dye-fibre bonds. Multiple studies investigated that the potential role of few natural dyes like curcumin and onion skin dye on fibre or fabric by providing UV protective characteristics. The combinational effect of dyes and UV absorbers together on fabric can also reduce the transmission of UVR. The dye shades substantially increase the UPF value of bleached cloth when compared with non-bleached fabric [43,46,74]. Although, light colours reflect solar radiation more efficiently than dark ones but part of the radiation penetrates more easily through the fabric. Since the dye’s absorption bands extend to UVR, all types of dye function as UV absorbers (280–400 nm). The capacity of dyes to raise a fabric’s UPF depends on the extinction coefficient. Another experimental result revealed that the colour depth and dye concentration are the most essential factors influencing the UV protection property of cotton knitted fabrics. Therefore, the UVR blocking ability of textiles are enhanced with increase in ingredient concentration with either a dye or pigment or a delustering agents or other additives [80,81]. :::

But the construction of clothing (how dense or thick the weave is) and what it’s made of appears to matter more for UV blocking overall than the color does. Cotton, linen and Rayon for example appear to offer less protection than wool, polyester, or nylon (synthetics feel kinda gross to wear in hot weather though, IMO). A blend can help make-up for that, though then there’s the problem of microplastics every time you wash them, so personally I still stick with natural fibers.