Yes vinegar does work great to remove hard water stains.
When using vinegar for hard water stains it's also best to have and use rubber gloves, a spray bottle, a cloth, and a spare toothbrush.
Put vinegar into a spray bottle and then spray the hard water stain with the vinegar and allow it to sit for 10 minutes or so.
Then take a toothbrush and scrub the hard water stain and it should start coming out of the clothing.
If not spray the hard water stain some more and allow it to sit longer and you may have to spray more vinegar onto the hard water stain.
After you allow the vinegar to sit on the hard water stain then take the toothbrush and scrub the hard water stain again.
Do that until it comes out but usually the first try the hard water stain comes out.
Then take a wash cloth and dip it in some water and then dab the hard water stain with it to help remove the rest of the hard water stain that came out.
After that wash the clothing or laundry as usually using your regular laundry detergent.