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.