I checked with my husband because he grew up Quaker and I married in (more to it than that, but simplified). He also said he hadn’t heard that. He looked it up and said the main similarities between anabaptists and Quaker’s is pacifism and Congregationalism.
I did ask the pastor about baptism and communion when I started attending the Quaker church. He said that the Quaker denomination is not against those things. They just don’t practice them ritually. He said it goes back to the 1800s when there was a lot of legalism surrounding the elements, and people believing that they were necessary for salvation. The leaders of the Quaker's decided back then to take the focus off of baptism and communion in favor of more focus on the work of the Lord in our hearts. Our church has done communion twice over the last year, and they are willing to do baptism on request. Due to water access here, that does not happen often. We don’t have a baptismal, and it is a drive to the nearest lake.
There is a range of levels around how conservative the church should be within the Quaker denomination (referred to as the yearly meeting). Actually, our yearly meeting split around 7 years ago over the issue of homosexuality. Those in the older generation especially do not drink or dance (we do not discuss my wine with my in-laws!!). Clothing is supposed to be modest, but there is no specific rule about what that means. Women don’t have to wear skirts or caps. Some women have nearly shaved heads, some have long hair. Color is up to preference too, although it is rare in our area for women to color their hair anything other than a natural hair color. I think that has more to do with the culture of rural living than anything, though.
So no, to sum up, there really isn’t a connection with anabaptists, although we do get along (as we do with most other denominations).
