Higher bather load pools, such as commercial/public pools, are a different animal. In those, one can have many more intermediate chlorinated by-products and some of these may be irritating. For Amanda's customer, it sounds more like a residential pool and at typical low bather load the chlorine itself *might* be irritating, depending on its level, but for most people it is not. Most tap water is chlorinated, so if this customer showers or takes baths and doesn't get irritation then they might not actually have a problem with chlorine (unless the tap water is chloraminated, which is monochloramine).

I just know that my wife hates swimming in our community center indoor pool over the winter because her swimsuits only last one season (elasticity gets shot) and her skin gets flakier and hair frizzier (though she never complained of irritation). In our own pool during the summer, none of these problems occur and her swim suits last for many years. The main difference is that the indoor pool has 1-2 ppm FC (sometimes more) with no CYA while our outdoor pool has 3-6 ppm FC with 40 ppm CYA which has the same active chlorine level as roughly 0.1 ppm FC with no CYA so a 10-20x difference. More than enough to account for at least the swimsuit degradation difference.

Anyway, if the customer truly does not want to use a halogen-based system (i.e. chlorine or bromine), then for pools the only other EPA-approved option is Baquacil/biguanide/PHMB with its own issues (and Amanda is in Spain where the regs are different anyway). For algae control, Polyquat 60 algicide used weekly should help.