Sheets?

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White on white in white. As wrinkle free as possible. Just got my new ones from Sears. We'll see how they wash up. Fingers crossed. As always if anyone has reached the holy grail of truly no-iron, Please post.
BTW I tried part polyester percale for our vacation rental. M u c h more difficult to remove stains. I'll trade a little more time with the iron with 100% cotton over how hard it is on my hands to do some of the stain removal on the percale.
I hear what you're saying but I just can't feel what I'm doing well enough if I wear gloves..

The weave shouldn't really have anything to do with it.
Muslin usually has a thread count of under 160 and is a loosely woven fabric, 1 over 1 under and personally, I find it close to sandpaper, even if you do use fabric softeners.
Percale has a thread count of 160 or above, tightly woven, 1 over 1 under, medium weight.
Sateen is 4 over 1 under. It should have a better sheen and be softer because of the weave.
Supima and Pima are a type of cotton, with Supima being a trademarked name licenced to mills.
Poly/Cotton usually does very well in washing, but it's always best to look for fabrics marked as stain-release or easy-care, which are chemically treated to wash well.
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I don't think it is the weave. It just seems that oily (lotion and the like) stains are more difficult to get out of polyester fabric. On the other hand, I have a stain release table cloth that a l w a y s comes clean, and its the one I take to fundraisers. I always expect I won't be able to get it clean, but all comes out in the wash every time. I've had that for over a decade. The problem sheets were purchased last year. Go figure.
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Grease can always be a difficult stain, hence the soil release finish. Have you tried shout for grease stains?