The lack of salt in tap water is likely the cause of eye irritation and redness. The concentration of salt in tap water about 2% of human tears. The concentration in chlorinated pool water is closer to 30% of human tears. Perfectly clean and balanced pool water should be less of an irritant than tap water.

https://www.aao.org/eye-health/ask-ophthalmologist-q/is-it-o...

https://blog.hayward-pool.com/maintenance/how-much-salt-do-y...