I love white cotton pillow cases but find that oily faces and hair can leave a yellowishness, so each bed change the pillowcases soak overnight in a bucket of very hot water with a couple or more heaped TBS of washing soda added. Into the wash the next day and they come out lovely.
I also use an Eco Egg for some washes which means no gunk from washing liquid, although I love BioD laundry liquid.
I am concerned about the ads for washing on very low temperatures as there must be a gradual build up of unpleasantnesses and bugs.
Top tip for those items which can have a long term niff eg dog bedding - just add a glug of white vinegar to the conditioner drawer.
Household cleaning spray - one part white vinegar, 2 parts water, small squirt of washing up liquid and a few drops of eg lavender. Or into a large jar filled with white vinegar collect citrus peels, squash into jar and leave for 2 weeks, the natural oils will leach into the vinegar and all you have to do is sieve out the bits and follow the above formula. Alchemy - and dirt cheap. (Sorry about the pun).