How do you get rid of the film caused by soy milk on drinking glasses?

That white film is either limestone deposited from hard water or powder detergent residue.

Soaking the glassware in white vinegar (acetic acid) and water overnight should work. Commercial products such as Lime-Away work well also.

After this use a rinse agent to prevent water spots from forming. Water softener is also a good idea (not for drinking though). Lastly, hand dry the glassware with a soft cotton towel whenever possible, especially fine crystal and stimware.