When I first got into the contra and traditional square dance
scene in Pittsburgh, PA, in the early 1980s, it was common not
to take right hands while crossing the set during a Right and
Left Through. No hands was also the usual styling in the
Boston area at that time. Ditto in the San Francisco Bay area
when I moved there a few years later. I think that in Seattle
at that time, they did use right hands.
In the SF Bay area today, using hands is by far the predominant
style. Part of the reason may be that at some point local
caller Charlie Fenton (then programmer for the San Francisco
contra series and frequent caller there and elsewhere in the
area) decided he preferred that style and began actively
promoting it.
During visits to New England in recent years, I've noticed
that I encounter the "with hands" styling much more often than
I used to. See, for example, these videos:
https://www.youtube.com/watch?v=z35S6tc5xqk
(NEFFA, April 2015; first R< seen about 0:57)
https://www.youtube.com/watch?v=zn4Hs8qWe-c
(NEFFA, April 2015; first R< about 2:34)
https://www.youtube.com/watch?v=pW72Qx11CMQ
(NEFFA, Arpil 2015; first R< about 0:23)
https://www.youtube.com/watch?v=W8zqG4688XI
(Cpncord (MA) Scout House; Sept. 2013;
first R< seen about 2:03)
https://www.youtube.com/watch?v=3GDAeExsj_k
(Scout House, Jan 2013; first R< about 0:30)
By contrast, look at this video from a dance at the Concord
Scout House in 1992:
https://www.youtube.com/watch?v=OPxhcI7jtnE
(Concord Scout House, 1992; first R&T about 2:06)
I don't know the causes of this shift in styling, and I'm
not stating a personal preference. I'm just reporting
observations. There may also be some communities where the
"no hands" styling is still firmly predominant.
By the way, both the stylings have long histories. Lloyd
Shaw's description of "right and left tHrough" in _Cowboy
Dances_ (p. 127) says
Each dancer gives his right hand to the opposite ...
but he later adds
Experts usually leave out the handshake, but beginners
find it a help.
I'm quoting from a 1950 edition of the book, but I think
those passages are unchanged from the 1939 first edition.
Historically "right and left through" derive (I believe)
from the circular hey for four, and I think that was done
in versions with and without hands in the time of Playford.
--Jim