Have Heard of European/UK Housewives
That gave their husband's marching orders to bring back nylon linens when they travelled to the USA on business trips. That and or they purchased lots themselves when on this side of the pond for holiday. Again one can only imagine the idea of "easy care" came as a welcome relief from generations of laundering all that linen.
Nylon is *very* flammable and thus not the best thing for bedding, especially for infants and children unless treated to be flame retardant (if possible). Indeed early airline hostesses wore stockings made from silk because that fiber is less likely to burn than nylon. This was a huge safety bonus to stewardesses since a fire onboard could mean nylons could literally melt onto the skin of their legs.
As for cotton/poly blend bedding, you find tons of it at thrifts, estate sales and so forth, and quite a lot NIB.
Cotton/poly blends came about as part of the "easy care" revolution of the 1960's and 1970's that brought us polyester leisure suits. Depending upon the ratio of cotton to polyester such sheets and pillow slips would need little to no tumble drying (polyester is a hydrophobic fiber), and usually no ironing (polyester is also thermoplastic).
Cotton/polyester bedding was also meant to replace the previous entry point for linens; heavy cotton muslin.
Cotton muslin sheets and pillow cases though very long wearing are a pain to launder and iron (trust us, we know). Because the threads are thicker they absorb lots of water. That water must be spun out, then dried to a certain degree before ironing, and make no mistake you would be ironing muslin sheets. Leaving any sort of bed linen in those days not ironed was considered "poverty" and or a sign of sloppy housekeeping. Also muslin linens feel so much better when smoothed by ironing.
Sending laundry out solved the problem of the bother of dealing with muslin on laundry day but could become expensive. Commercial laundries often charged by weight of bundle. This means heavy sheets and pillow slips cost more to service than say percale. Indeed today many laundries that do hotel, hospital and other such bed linens often insist upon a certain blend of cotton/polyester because it makes for easier processing than pure cotton muslin. The establishments themselves see a reduction in cost because of the aforementioned difference in weight. Cannot recall the last time one saw pure cotton muslin sheets in a hospital or other healthcare facility, though one assumes they are out there.
Thing about polyester is that because it resists water it can be very difficult to get clean. Oils and certain stains do not shift easily either. All this is compounded by the fact polyester being a thermoplastic fiber cannot withstand very hot washes. As things stand you have to use various "permanent press" or "easy care" cycles with warm or barely hot water to prevent new creased from being set in for good.
To an extent the same problem happens with cotton/Lycra blends. Those Prada and other European men's shirts look great at first, but since they usually are dry clean only do not stay "fresh" and "clean" looking for long. Whites in particular can start to turn gray and dingy.