I finally, after all these years found out what the "Hugging Molly" was. I ordered a book called Gumbo Ya Ya off the internet. it was first published in 1945. It has all kinds of Louisianna folk lore in it.
The Hugging Molly was in there. The HM was actually a mentally disturbed man who would hug women on the street. He dressed up in a white sheet or robe and would very strongly hug women at random. He never hurt anyone, but many black women were afraid of him because the white robe or sheet made them think he was part of the clan.