I haven't seen that particular approach or line of argument in gay rights rhetoric. By and large, the gay rights movement seems to benefit more from the government - at least segments of the judiciary - than from the electorate. On both the state and federal level.
A refusal to pay taxes on moral protest grounds does harken back to Thoreau's opposition to the Mexican American War, however - as chronicled in his 1849 piece, "Civil Disobedience."
I'm not sure if the sign was directed at the federal government for keeping DOMA on the books or targeted at individuals in California living under Proposition 8. Or in Wisconsin after the state's 2006 constitutional marriage amendment.