Actually the problem here can partly be blamed on the state of your washing machine. Check inside the rubber seal behind the door, it’s probably full of black gunk, bacteria. The solution is simple. Clean the gunk out and Do an empty boil wash with a cup of vinegar to clean the machine.
I found that my towels used to smell once I had used the a few times, not any more! And no, your clothes won’t smell of vinegar.