The right side of politics will in most places will usually be opposed, or at least uninterested in gay marriage issues - and the converse for the left.
This is because the right is usually more focused on the good of the nation; and the left is usually focused more on the good of individuals. Both approaches aim at general wellbeing: the right, through raising the entire standard of living, so that the poorest are much better off than the middle-class in other nations; the left, noting that the rich and middle-class are already fairly well-off focus their improvements directly are the poorer/disadvantaged/marginalised.
In its extreme, the right places the good of the nation at such great importance, so that individual good is sometimes negatively forfeited; and the left in its extreme places the good of the poor so high, as to ruin a nation, as it were dragging everyone down to the level of the worst-off; and this can spiral into increasingly worse conditions for everyone.
Center politics, as much as that every really exists, focuses on the good of the middle-class majority; such that unusual concessions are made neither to the extremely well-off, nor to the extremely disadvantaged. Permitting these distinctions/traits, it would seem that gay-marriage agendas can normally only ever be associated with the left (or the extreme left) of politics. This being because the gay marriage lobby is focused at a very small group of committed couples, which perceives itself to be socially/economically disadvantaged - and seeks outcomes which fundamentally redefine the status of the vast majority of committed couples (heterosexual couples). Uncommited couples are a somewhat seperate issue.
(Of course, this is a matter of social left and right, which doesn't always correspond with the economic, military, etc leanings of a particular political entity).
