Ok! I think you are on to something. It sure looks like something a baptismal gown would be made of.
So it doesn't have one all encompassing name then. It's batiste fabric with eyelet. Cool!! Thanks! (I would not have figured that out myself)
Oh, not muslin. Not sure about broadcloth. I think shirting would be thicker?? It's very soft and on the thin side. Maybe it could be used for a woman's shirt.