I believe that it is undesirable to ingest excessive amounts of chlorides.
Normally, the amount of chloride intake should not exceed the amount of sodium intake, i.e. one should not ingest other chlorides except table salt. The normal amount of chloride in the body is less than that of sodium, a part of the sodium ions being neutralized by bicarbonate anions. Any excess chloride requires additional work for the kidneys, to eliminate it from the body. Excreting chloride is also likely to take with it some of the useful metallic cations that you have supplemented.
Other metallic cations than sodium should be combined with organic anions, i.e. one should ingest their salts made with organic acids chosen from normal nutrients.
Good choices are potassium citrate (one of the cheapest organic acids that is also a normal component of food) and magnesium bisglycinate (because the magnesium salts of cheaper organic acids, like citric acid, are not soluble in water, while magnesium bisglycinate not only is soluble in water, but it also does not form solid precipitates with other components of food, which would prevent its absorption in the gut).
Both potassium citrate and magnesium bisglycinate can be found as cheap pure powders, which are preferable to any other forms, like capsules, which contain useless excipients for which there is no reason to be introduced in your body.
Besides sodium, the only other exception to the rule of using salts of organic acids is calcium, which can be supplemented as calcium phosphate or bone meal. However, calcium phosphate powder is not soluble in water, so unlike sodium and magnesium salts powders it cannot be put in drinking water, but it should be mixed like table salt in some solid food, before eating it.
It's worth noting that glycine can have negative psychological effects on some people, anxiety, insomnia, etc. Supposedly it's because it's a NMDA receptor co agonist.
The amount of glycine that accompanies the at most a few hundred milligrams of magnesium per day that you might want to use as supplement is relatively small in comparison with the glycine content of most kinds of food that you eat anyway.
Bisglycinate is the cheapest form of chelate magnesium, but there are somewhat more expensive forms of chelate magnesium, which use other amino-acids instead of glycine. Someone who is very sensitive to glycine could use those. The non-chelate forms of magnesium are prone to form solid precipitates that pass through the gut without being absorbed.
Much more glycine than in a Mg supplement would be provided by any food with gelatin, so if someone really has glycine sensitivity, that should manifest when eating food with gelatin.