Two? I see FamilyReligion but I dunno what your other one is. But to test family & MoralViews:

R> lw <- read.csv("2012.csv")
R> lwr <- subset(lw, as.character(FamilyReligion) != " ")
R> lwr <- subset(lwr, as.character(MoralViews) != " " & as.character(MoralViews) != "Other / no answer")
R> levels(lwr$FamilyReligion); levels(lwr$MoralViews)
[1] " " "Agnostic" "Atheist and not spiritual"
[4] "Atheist but spiritual" "Committed theist" "Deist/Pantheist/etc"
[7] "Lukewarm theist" "Mixed / Other"
[1] " " "Accept / lean toward consequentialism"
[3] "Accept / lean toward deontology" "Accept / lean toward virtue ethics"
[5] "Other / no answer"
R>
R> cor.test(as.integer(lwr$FamilyReligion), as.integer(lwr$MoralViews))
Pearson's product-moment correlation
data: as.integer(lwr$FamilyReligion) and as.integer(lwr$MoralViews)
t = -0.6631, df = 858, p-value = 0.5075
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.08935 0.04429
sample estimates:
cor
-0.02263

I wondered if maybe the levels were screwing things up, even though they're in a logical order which should show any correlation if it exists, so I binned all the results into just binary 'atheist' and 'theist' (as it were), and looked at a chi-squared:

R> fr <- sapply(as.integer(lwr$FamilyReligion), function(x) if(x>4) {1} else {0})
R> mv <- sapply(as.integer(lwr$MoralViews), function(x) if(x>2) {1} else {0})
R> ct <- chisq.test(fr,mv); ct
Pearson's Chi-squared test with Yates' continuity correction
data: fr and mv
X-squared = 2e-04, df = 1, p-value = 0.9894
R> ct$expected; ct$observed
mv
fr 0 1
0 200.6 58.43
1 465.4 135.57
mv
fr 0 1
0 200 59
1 466 135

I am a little surprised. Maybe I messed up somehow.