Tide and Persil... household here...
We all have sensitive skin... I do alot of double washing due to it, and even have to add a extra rinse cycle just to make sure everything is out of the clothes, and towels ... My grandson skin is super sensitive, tide only with a extra rinse cycle for all his clothing...
I use the Persil, on DH's white undershirts, wash in Persil and bleach, then in Tide... then dryer...
We have a boat, so any of the clothes and towels after a weekend on the water, get washed in Persil first then re-washed in Tide.... to get the all the sunscreen, and sweat and salt & brackish water, or river or lake water, plus if we are fishing... they get a funky smell to them, ... and then everything smells and looks really clean...