I think what was called cheesecloth in the UK we called cotton gauze or even "crinkly cotton gauze" in the US. I remember seeing shirts made out of it, identical for men and women, from the late 60s through the mid-70s, almost always in "natural" colors, meaning off-white to cream to beige. A lot of them had like flower or vine embroidery around the neck in almost the same color as the fabric. I mostly remember crinkly cotton gauze used in women's peasant skirts and sundresses, which stayed popular until about 1978. These were from just below the knee to floor-length and usually white, but some had tiers of different muted, pastel colors edged in eyelet lace. Worn with wedge-heeled sandals or ankle-wrapped jute espadrilles.