Let's say some chemical washed out the pigments in our skin
This is simply oculocutaneous albinism. Wikipedia states that "Albinism in humans is a congenital disorder characterized by the complete or partial absence of pigment in the skin, hair and eyes." However, this doesn't give you the ability of seeing albinos' internal organs, because you would still have fat and blood underneath.
However, a chemical has actually been developed to make tissue transparent, and its name is Scale. This article gives a good summary of what you need for a body to become transparent:
“For transparency, you have to get rid of scattering,” says Duke University biologist Sönke Johnsen. After 15 years of studying transparent sea creatures, he admits scientists still do not know exactly how certain animals allow light to travel through them. But he does know what ruins transparency: “We observe light when it moves from one refractive index to another. The more indexes it moves through, the more scattering there is.” The varying refractive indices of skin, muscle, and bones make most animals opaque. Scale works by soaking into the cells and creating a uniform refractive index that photons pass through.
I highly doubt that the use of Scale is compatible with life. However, let's pretend it is and let's take a look on what would the medical consequences of having internal organs exposed to sunlight be.
- Melanin, the pigment lacking in albinism, protects our skin from ultraviolet radiation, which causes DNA to mutate. As such, albinos are more prone to melanome development. I'd guess that having internal organs exposed to UV radiation means an increased risk to cancer development, at least for those not encased in bone.
- On the other hand, detecting cancer (or at least the macroscopic ones) would be easier - the only things physicians will need will be a good flashlight.
- Eyelids would be transparent as well. I think this could produce eyes conditions and sleep deprivation problems.
I guess there will be also a change in aesthetics - suddenly, appearance of people involves a beautiful intestine or an elegant bladder. There will be cosmetics for the enhancement of internal organs looks. Also, probably chewed food won't be gross anymore, as we would be able to see it each time someone eats. In short, perception of what's beautiful and what's ugly would change pretty drastically.