Why do Irish swimming pools require bathers to wear hats?

It REALLY has nothing to do with hygiene, as most people are told (to shut them up, obviously). I'll give you a layman's explanation and avoid all those terms I had to deal with when I taught lifesaving and pool maintenance several decades ago.

The reason is that the scalp has oils that can be released in the water; when the water is recycled through the pool filter, it first goes through a hair strainer (that catches hair, bubble gum, hair pins and other such matters). The reason is to keep the filter from having to be backwashed (to rid the pool filter of matter or debris caught in the filter bed) frequently.

Now, believe it or not, the filter forms a beneficial mucous substance, called "floc," that is the result of the sodium carbonate (often called "soda ash"), which causes the water to become alkaline (to prevent acidity that corrodes metal parts of the pool pipes and machinery) together with the chlorine forms the "floc" that catches tiny matter that would otherwise pass through the filter bed and cause the water to become slightly murky or cloudy... really unsightly and reduces visibility. The body oils (which is why people are required to shower BEFORE entering the pool water) and the scalp oils hamper the filter bed floc and prevents it from catching the tiny matter that would otherwise be caught by the floc.

Now, every time the filter is backwashed, lots of water is lost and chemicals, and water must be added to the pool to maintain a proper level (which costs a lot of money at the end of the year). The more oils in the filter bed, the more frequent the filter must be backwashed, as indicated by the inflor and outflow gauges on the filter body. That's why caps are required and showering before entering the pool. Plus, it keeps the funk from people's body from entering the pool... how do you feel knowing that water spashes into your eyes, ears, mouth (and other body cavities) that comes from people who do not shower frequently or may have NOT properly wiped the excrement from their butt orifice? Ugh!

If it is a hygiene code that has to be followed, that is the law. There are a lot of pools where swimmers with hair over 2 inches past their earlobes, a swim cap is required. I try to keep my hair short, but I will wear a swim cap even with short hair.

The more swimmers without hats, the more often the pool filter needs to be cleaned, if not outright changed. It's a maintenance thing...NOT a hygiene thing.

Pool filters can be expensive. Keeping stray hairs out of those filters allows them to work properly for a longer period of time, thus not needing to be changed/cleaned as often. Which saves the hotel money so that they don't have to end up charging YOU for it (i.e. they don't have to make the room rates higher to afford those extra filters they'd have to go through without that rule).

Maybe it's a hygene thing. Maybe your hair could add germs or pick it up or something.

it is to do with Hygiene

Why are you stupid?