Quick Answer
Pool water is heavily chlorinated (parts-per-million scale), while municipal tap water is lightly chlorinated (fraction of a ppm). Showering before the pool is a hygiene courtesy; showering after rinses pool chlorine off your skin. Municipal shower filtration reduces tap chlorine, not pool chemistry.
Problem
Swimmers conflate pool chlorine (high) with tap chlorine (low) and expect shower filters to address both.
Product Recommendation
ZOOSHEN filters reduce the low-level chlorine/chloramine in your home shower water. See /technical/chlorine for what municipal residuals are.