"Just because you believe that gay rights are as fundamental as women's suffrage does not mean that, as a political issue, gay rights are as decided nationwide as women's suffrage."
That's exactly what that part of your sentence says, unless I am reading this incorrectly.
I think you're reading it incorrectly. You're interpreting it backwards from what I intended.
X = "you believe that gay rights are as fundamental as women's suffrage"
Y = "gay rights are as decided nationwide as women's suffrage"
All I wrote is that X does not imply Y. You seen to be interpreting it, though, as (not Y) implies (not X), the contrapositive of which is X does imply Y, which is basically the opposite of what I meant.
That's exactly what that part of your sentence says, unless I am reading this incorrectly.