Even in those systems the positions on capitalism are on the horizontal, left to right axis. Because when talking about politics left and right are used to describe positions on capitalism.
Neoliberalism is a pro capitalism ideology therefore it’s a right wing ideology.
That people may not hold political ideologies is irrelevant to neoliberalism being a right Wong ideology. Its also not a new phenomenon by any means.
I 've seen it. You want to rename the axes. The US Democrats are socially progressive right wingers, Zapatero is socially progressive left winger.
I am also not denying that there different dimensions of politics ideologies and that people can hold different combinations of them.
But neoliberalism is a position in the left-right axis. On the right. If you describe someone as a neoliberal you are describing a right winger. They might be socially progressive or they might not be. I also expect that whatever else they are they will primarily act based on their neoliberal convictions. Just like I expect the US Democrats (at least the high profile officials and politicians) to put neo liberalism before social progress.