It depends upon one defines a social conservative, since like any other catchall phrase looses a lot of detail if it is bandied around without context.
If we look at a few keys subjects commonly considered part of the "social conservative" movement like Abortion Rights, Gay Marriage, and Gun restrictions we see a considerable amount of variation within the six states of New England....
From most socially conservative to less socially conservative:
1.) Abortion Rights
A.) Rhode Island--- 63% PRO
B.) Maine---- 64% PRO
C.) New Hampshire 66% PRO
D.) Connetticutt 67% PRO
E.) Vermont 70% PRO
F.) Massachusetts 74% PRO
2.) Gay Marriage
A.) Maine--- 63% PRO
B/C VT/CT--- 67 % PRO
D.) RI--- 70% PRO
E.) MA--- 73% PRO
F.) NH---- 75% PRO
3.) Support for greater gun restrictions....
A.) NH--- 54%
B.) ME-- 55 % (Wide gap between ME-01 and ME-02 here)
C.) VT--- 59%
D.) RI/MA/CT roughly between 62-67% depending upon CD
So if we look at abortion, gay marriage, and guns as the core parts of social conservatism, it appears that Maine places towards the top of all three categories....
The water is much muddier as for the 2nd / 3rd string contenders...
It definitely looks like Mass. is the least socially conservative state in New England on these issues, and if it wasn't for CT's relatively lackluster support for Gay Marriage, I would probably put at as the second most socially liberal state in New England....
Anyone want to chime in with some other metrics and themes of social conservatism that I didn't reference above based on public polling numbers by state?
Did you just make thise numbers up?
No... numbers regarding Abortion are from a Pew poll from 2014...
http://www.pewforum.org/religious-landscape-study/compare/views-about-abortion/by/state/
Numbers regarding Gay Marriage is from a Public Religion Research Institute (PRRI) national survey from 2015.
http://www.prri.org/spotlight/map-every-states-opinion-on-same-sex-marriage/
You could look at the Williams Institute (UCLA ) survey by state from 2012 which shows a slightly different pattern, but one would surmise that on this issue as public attitudes have shifted dramatically in just the past few years, the most recent data would be more representative.
http://williamsinstitute.law.ucla.edu/research/marriage-and-couples-rights/public-support-for-marriage-for-same-sex-couples-by-state/
The data on support/opposition for great gun restrictions is from July 2016, and is actually broken down by CD.
https://www.isidewith.com/map/2Y5/support-for-gun-control#z5
The abortion numbers are interesting, but they look a little too favorable to "legal" overall, when compared to Gallup's most of the time equivalent question. Plus, there are a couple that look wrong at first glance, like Oklahoma and Nebraska being underwater.
These numbers come out to always/mostly legal +14, while others, such as CNN have it always/mostly illegal +18. It really depends on the exact wording of the question. Gallup has pro-life/pro-choice tied over the last couple years, so here is a map with these state numbers indexed to a tied nation: