You aren't drinking the pool water so the comparison with your whole house filter isn't quite valid. Also, your water district may be using monochloramine (chloramination) and not chlorine (hypochlorous acid; chlorination).
You use Cyanuric Acid (CYA) in your pool so most of the chlorine (around 97% or so depending on CYA level) is bound to it. CYA has virtually no skin absorption (see
this link) so chlorine bound to CYA should be similar and is not volatile so the actual active chlorine level in your pool is equivalent to roughly 0.1 ppm FC with no CYA so around 1/10th what would be in chlorinated tap water. Chlorine itself is not the health concern -- it is the chlorinated disinfection by-products when chlorine combines with ammonia to from inorganic chloramines (especially nitrogen trichloride aka trichloramine) and when it combines with some organics.
As for various studies on chlorine's effects in swimming pools, the studies are nearly all about indoor commercial/public pools because that is where there is a combination of high bather load, lower air circulation, and lack of sunlight (so lack of UV) that create the worst conditions for creation of the highest levels of disinfection by-products (CYA is typically not used in indoor commercial/public pools so the active chlorine level is far higher as well). You can read the thread
Asthma and Chlorinated Pools, and part of the thread
New Chlorine Scare,
this post with a link to a summary of epidemiological studies for drinking water and
this post where I discuss various chlorine alternatives and their limitations.
Remember that residential pools have extremely low bather loads, are generally outdoors exposed to the UV in sunlight and with better air circulation.
There aren't any posts I can recall about any consequences to changing the skin's biome due to killing bacteria and reducing fungi that would otherwise be growing on the skin. For many people with skin conditions, chlorine helps them more than hurts them. Sensitivity to chlorine is extremely rare though possibly less so for monochloramine.