this is just incorrect. i understand that neoliberal has been overused as a term to the extent where people don't understand what it means, but if you are going to use it you have to understand it has absolutely nothing to do with socially liberal issues.
this is the definition of neoliberalism:
"Market-oriented reform policies such as "eliminating price controls, deregulating capital markets, lowering trade barriers" and reducing state influence in the economy, especially through privatization and austerity."
it is entirely used in reference to economic policy associated with economists like Friedman and Hayek
this is a phenomenon seen all over the world since the 1980s in politics that has no correlation with the social issues of politicians and political parties.
the two politicians most frequently associated with the rise of neoliberalism are Margaret Thatcher and Ronald Reagan, who were both intensely socially conservative and anti-gay.
other neoliberal politicians include Deng Xiaopeng, Recep Tayyip Erdogan, Bashar al-Assad, Boris Yeltsin and Jair Bolsonaro. None of these people advanced socially progressive or liberal policies at all. Now its possible for politicians to be neoliberal and more socially liberal - Tony Blair for example - but its not exclusive. Trump, McConnell and the entire Republican Party are neoliberal.