That's really the finding in a nutshell - the most popular chemical sunscreen Avobenzone - commonly regarded as safe forms toxic compounds with chlorinated pool water in the presence of UV radiation. Now I am not an alarmist re chemical sunscreen - it's better than nothing and not tacky and used more often as a result. Avobenzone especially is very popular and is unique among chemical sunscreens in terms of providing broad spectrum protection from UVB (burning rays) and UVA (aging rays) - it offers about 30 mins protection when exposed to sunlight but is not too stable and is usually stabilized by octocrylene which is only a UVB (burning ray) protector. There is almost no drugstore product that is without it and very often mineral sunscreens include avobenzone.
What you need to know is that this is a big deal when combined with chlorinated pool water it forms aromatic acids, aldehydes, phenols and acetyl benzenes - all not great for pool water which you frequently ingest if you're actually swimming rather than lolling around in a pool. The takeaways are basic - it's better to find physical sunscreens with only mineral sun protection and even better to wear rash guards to have more effective sun protection in the poolside or go in the evenings or early mornings when the UV index is not crazy high.