Actually, I think history reveals that the reverse is true. In the U.S. the Progressive Era and the New Deal preceded the Sexual Revolution by decades. Europe was flirting with socialism long before they reached their current level of sexual libertinism.
Furthermore, in the 1980's porn became much more accessible through cable and videocassettes. This trend continued in the 1990's and up to today with the internet. During this time causal sex became more acceptable in the media and in society, but was tempered somewhat by the AIDS crisis.
These same past two decades of sexual libertinism have been the era of Reagan, welfare reform, and tax cuts.
One of the reasons the left promotes sexual libertinism is because of its tendency to expand government power. For example, unleashed homosexuality leads to more hate crimes (thought crimes) laws, more laws dictating who people can hire, who they can have as members of their private clubs, who they can sell or rent property to, etc. Gay marriage will lead to an expansion of social security, etc.
Promiscuity causes more illegitimacy, which means more welfare, more single moms voting for socialism, etc.
James Madison was right. An immoral people cannot remain free. Tocqueville was also right when he attributed America's greatness at least partly to our better morals than those found in Europe.