Highfalutin talk about freedom being indivisible isn't much help here, if only because so many folk think otherwise. For every Guardianista who favours gay rights but dislikes economic liberty, there's a Conservative with the opposite preference.
Nor is UK history much guide. If we compare now to the 1970s, we probably have more economic liberty, by Tim's lights, than we did then and there's less homophobia, sexism and racism. That suggests a positive relationship between social and economic freedoms. But if we compare now to the late 19th century, we have less economic liberty but more freedom for women and gays. That suggests a negative relationship between economic and social freedom.
Luckily, a new paper by Niclas Berggren and Therese Nilsson sheds some light here. In a cross-country study of 65 countries, they find that economic freedom is significantly positively correlated with tolerance of homosexuals, but has no significant link with racial tolerance. Cynics might say this is because the selfishness generated by economic liberty causes people to care about house prices more, and gay people help to raise these, but I suspect this isn't the only story.
Curiously, there are two particular aspects of economic freedom that encourage tolerance of gays. One is legal protection of property rights, and the other is low and stable inflation; a credible inflation target reduces homophobia. The size of government, openness to trade and extent of regulation seem irrelevant. The authors say:
Stability, safety and an expectation of fairness (in the legal and monetary systems) are conducive to not regarding others as threatening.
There's something here, I think, for everyone. On the one hand, Guardianistas can point to the lack of link between economic liberty and many aspects of tolerance as evidence that economic liberty is separate from many social freedoms. But on the other hand, economic libertarians can point to the fact that there's no evidence that economic freedom reduces social liberties, and some evidence that, in one respect at least, it increases them.