First of all, water that we swim in is very different from the tears that usually bathe the surface of our eyes.
Swimming pool water is tapwater with added antialgal and other antimicrobial agents such as chlorine. And even though sea water contains various salts, the concentration and type of salts is also very different from that of tears.
One measure of concentration is osmolarity, which is a measure of all the solute particles in a litre of solution. Normal tear concentration in a non-dry eye state is below about 290 mOsm/l, while that of sea water is about 1000 mOsm/l. (Osmolarity of sea water)
While not always the case, swimming pool water often has certain contaminants we would not like in our eyes. (https://www.theguardian.com/science/2017/mar/01/how-much-pee-is-in-our-swimming-pools-new-urine-test-reveals-the-truth) Sea water is also often contaminated by run off from sewers, storm drains and discharge from ships.
So opening your eyes underwater may be OK for short periods in pristine environments but even so is likely to sting somewhat due to the much lower (swimming pool water) or much higher (sea water) concentration of salts. After a while, the vision may blur as well, due to excessive hydration or dehydration of the corneal epithelium and development of punctate erosions.
In short, yes, there are some risks to your eyes of irritation or infection if they are directly exposed to swimming pool water or sea water. It’s always better to have a pair of goggles on and minimise the amount of water that your eyes are exposed to.
