They spun it off as some other company, but yes Playtex made the garment components of the Apollo space suits. Hamilton-Standard built the PLSS backpack and machinery. Apparently Playtex had the most experience in the nation with making rubberized structural cloth products, and were thus able to engineer a suit that could both hold pressure, and allow the astronaut to freely move. The Mercury and Gemini suits, were made by BF Goodrich, and were so stiff and immobile that most of the fingers of the glove were curled to allow them to grip things, and the middle fingers were straight so they could effectively push buttons.

There's this hilarious documentary about the two companies working together on this contract; this serious faced old hemorrhoid of a man talking about "At Hamilton-Standard we manufactured aircraft power plant and propeller components for commercial and military applications. They made brassiers."

Later on they interview the chief seamstress whose team actually sewed the suits. "I was making baby pants. They came to me and asked if I wanted to try something a little different, and I said sure." "There had to be ten stitches to the inch. No less, or more. We would walk the sewing machines one stitch at a time." "You absolutely could not leave a pin in a garment, for it might hurt the astronaut, or even puncture the suit. So I issued each girl pins with different colored heads. I was inspecting a garment and found a red pin. I looked up which girl it was, and I walked over and said 'is this your pin?' She said 'no' and I said 'well here's your pin' and I stuck her in the behind with it."

The 60's were fucking wild, man.