In the past, I was engaged in synchronized swimming, 10 years old, MS.
Training took place for 3-4 hours in chlorinated water, it happened that all this time we trained without glasses. During this time, vision did not fall. But after such training, the eyes hurt, there was a white veil, and the squirrel became very red. Drops saved from eye redness and sleep. Neither me, nor any other athlete had any eye diseases.
I read about such a technique for improving vision: alternately open eyes in cold water and in water at room temperature. the author assured that good eyesight would return completely. I don't know if this method is effective, but nothing bad happened to me after a couple of attempts
When I lived in Evpatoria for a month, every day I swam on a wild beach and dived with my eyes open (all the time), my eyesight improved and my eyes got tired much slower from the computer monitor. (And I'm not kidding)
For about 15 years I have been diving with my eyes open in the Black Sea (a stone beach, there are relatively few people), my grandfather-doctor taught me to open my eyes in water for a long time, now my vision -3 is genetic, I have never had conjunctivitis.
For as long as I can remember, I have been swimming underwater with my eyes open. And in the pool, and in reservoirs, and at sea. And you know what? Vision, as it was 1, remained, neither conjunctivitis nor the like was noticed. Perhaps the reason is that I have been swimming since childhood (from about 4 years old) and, as long as I can remember, always with open eyes. Maybe the body has just adapted. I felt the maximum discomfort only once, when there was an opportunity not to get out of the pool for three hours)) To be fair, I will note that I was 10 years old then, and then my eyes were just very red and tingled a little.
Once I went with my parents to the sea to rest. And I am a man of water, so I like to dive with my eyes open. As a result, conjunctivitis started on the 5th day. Be careful with this.
I also live on the Volga all my life and swim in it (and other fresh water bodies) with open eyes under water, I did not notice any direct harm. Only, of course, at the very moment of diving you have to close your eyes, hitting the eyes with water is still a pleasure. True, I have myopia of -4 in both eyes (in childhood it was up to -6), but there are still a lot of bad habits that caused it, such as reading at dusk and lying down).
And here is the answer without any justification, just personal experience: I always dive when I swim, and always open my eyes to see where I am swimming. It is rather painful in the pool: the cornea becomes cloudy and reddens. In salt water, as a rule, it hurts from salt, although if the sea is not very salty, then it is normal (in Black, for example). Most of all I swim in fresh water - I live on the Volga. Every summer many, many times I dive into the Volga and open my eyes. They are tingled on the contrary, because the eye is saltier than water, but in my opinion this is the least discomfort. And over the years, nothing bad has happened to my eyes.
Let's first deal with the aquatic environment in question.
If we are talking about a pool in which water is purified with bleach, then we can safely conclude that swimming there with open eyes it will not lead to anything good, but only can cause irritation and unpleasant sensations of burning eyes. In some individual cases, acute conjunctivitis may occur. That is why it is necessary to swim there with glasses.
Let's go further. If we are talking about ordinary tap water, then it all depends on what kind of pipes you have, what water treatment system is installed, etc. In general, in Russia the situation with tap water is more or less normal. But this water is also purified by chlorine, so see for yourself. Once I opened my eyes in the bathroom, as if nothing had happened.
In nearby water bodies, opening your eyes while swimming can be very dangerous, because various chemical wastes can merge there. But if you are sure that the water is 100% clean there and nothing flows there + there are no signs of contamination, you can try to open your eyes for a short time.
And now about the most important thing - is it possible to open your eyes when you swim in the sea? It seems to me that everything depends again (yes, yes, yes) on the level of water pollution. I swam once this summer in one of the seas of the Primorsky Territory, then my whole body was covered with small spots of fuel oil (you see, the tanker leaked or something like that). But if we take pure seawater, then it is in principle harmless to open our eyes there, but it is worth doing it gradually, in moderation and a little bit, so as not to cause a sharp response from the protective system of the eye. The main thing is not to get into the eyes of marine debris in the form of pieces of algae, sand, etc.
However, in any case, physics will take its toll, and you, being with your eyes open in the water, will see everything blurry due to refractive properties.