I always double rinse my laundry. Well, not the towels or dishcloths, or throw rugs, but everything else.
Another thing is that I have given up on cold water washing and rinsing - always warm. I found a laundry chart that had various definitions and the one that jumped out at me was the temperatures. Warm was 95 degrees and cold was 80 degrees. That is way different from the water department's 50 degrees for cold water. If I took the time to put in a mixer on the cold water side to add some hot water to raise it up to 80° it might work, but 50° water just never got stuff clean if there was any real dirt on it. If I have something that demands cold water I just turn down the hot water knob so the washing machine's warm mixture is cooler.
The real problem is using too much detergent in the first place. It doesn’t take much. We use about 1/3 - 1/2 of the recommended amount. Using too much helps the clothes become re-soiled much more easily because of the detergent residue left behind.
Carpet cleaners have known this for at least the last 35 years.