The problem with the dingy clothes is that modern washing machines don’t produce enough agitation to truly utilize laundry soap. This is why stores primarily sell laundry detergent. Basically a low grade residue is being left on the fibers every time you wash them with the laundry soap. This gradually builds up and then starts preventing them from getting clean. It builds up faster if you have hard water.
To get your clothes clean again you will have to strip them. It is hard on the fabrics so should not be done too often.
To prevent this in the future you have a couple of options. Option 1, use an old washboard or other super agitation method like plungers in a bucket to wash your clothes. This allows the soap to actually function as intended. Option 2, alternate between one load with soap and one liad with detergent. This will prevent the build up as the detergent can gently strip it before it becomes an issue. Option 3, if you have soft water you can add vinegar to the fabric softener portion of your cycle. This will act similarly to the detergent and lift any residue.