The state's reputation as a cultural backwater, has been transformed by the Museum of Old and New Art (Mona), which opened in Hobart in 2011. Featuring the private art collection of a professional gambler, multi-millionaire David Walsh, Mona has attracted more than 250,000 visitors in its first year.
Tasmanians could be forgiven for pinching themselves, so radically have things changed in little over a decade. But they, too, have changed. In 1988, support for decriminalising homosexuality was 15 per cent below the national figure. Recent polls found support for same-sex marriage to be 5 or 6 per cent higher than nationally.
In a cafe in Salamanca Place, Rodney Croome, spokesman for the Tasmanian Gay and Lesbian Rights Group, recalls rallies for and against decriminalisation. The latter resounded to chants of "Kill them, kill them" - and some politicians called for the death penalty to be reinstated for gay men. During the market stall protests, 130 people were arrested in seven weeks. (Croome was arrested four times.) The state had repressive laws, carrying higher penalties than elsewhere in Australia - a phenomenon Croome attributes to its convict origins, and the association between convicts and homosexuality.
Politicians shrugged off condemnation by Amnesty International and the UN's Human Rights Committee, as well as a boycott of Tasmanian produce by mainland restaurateurs. Only when the case went to the High Court did Parliament give way in 1997.
Those who welcome a more progressive Tasmania note that the seeds were planted long ago. In the 1970s, the state was the birthplace of modern Aboriginal politics, with protest marches leading to the recognition of Tasmanian Aboriginal identity and the burying of a century-old myth that the race became extinct in 1876 with the death of Truganini, the last full-blooded Aborigine.
It was also the cradle of the global environmental movement, with the world's first Green party created there in 1972. A place of pristine wildernesses and outstanding natural beauty, it was at the same time (and until recently) the site of rapacious logging of old-growth native forests. To the outside world, Tasmanians were greenies or rednecks, although the reality was more nuanced.
"If you look at the forestry issue, in particular, it's a battle for the Tasmanian soul, and that's what has underpinned politics here for a long time," says Cassy O'Connor, a Greens minister in Lara Giddings's Cabinet.
Croome grew up on a dairy farm in the state's north-west. When he was at university in the early 1980s, police would monitor gay community meetings and record the registration numbers of those who attended. Now, "my very large and conservative extended family are very accepting of me and my partner, and they support this [same-sex marriage] reform, because they want me to get married".
The law was defeated in the Upper House by just two votes. In stark contrast, similar legislation was crushed 98-48 in the federal House of Representatives in September. New South Wales, South Australia and the Australian Capital Territory all plan to introduce bills next year.
Tasmania has led the way in recognising same-sex relationships, permitting civil unions and legislating for same-sex adoption and surrogacy. "Now people talk about the 'Tasmanian moment' or the 'Mona moment', meaning that Tasmania is beginning to fulfil its potential for innovation and creativity, openness and inclusion," said Croome.
O'Connor said: "I actually think Mona changed the way a lot of Tasmanians think about this place. Because suddenly the eyes of the cultural world were on us, and we have here in Hobart this amazing cultural institution of international value."
Not everyone sees things that way. While acknowledging that Tasmanian society has "changed greatly", Hobart-based novelist Richard Flanagan says: "We've still got a conservative polity." He cites Giddings's backing for a controversial pulp mill in a scenic valley, the building of a motorway across a site containing 40,000-year-old Aboriginal artefacts, and the Government's strong endorsement of mining in the temperate rainforest of the Tarkine - all policies, he says, that are "backward, divisive and unnecessary".
One factor often missing from the debate, according to Flanagan, is the poverty of ordinary Tasmanians. "On all indices this is the poorest society in the Australian federation." Advocates of same-sex marriage say it would boost tourism and the the ailing economy. Walsh is keen to host weddings at MONA, envisaging a Hotel Mona, or HoMo.
Until 1997, Tasmanians who wanted to to be openly gay mostly emigrated to Melbourne or Sydney. Now they need no longer become "sexual refugees", says Croome, adding that while the campaigns of the 1990s were about privacy and equality, "for me and many others it was much more about belonging".