Reagan undeniably paved the way for Christian nationalism to take over the republican party.
I disagree on Thatcher and Howard accelerating fundamentalism, though neoliberalism is a fair call. You were damned if you did or didn't and Hawke/Keating set a lot of reforms in motion prior to Howard. We weren't equipped to cope with global changes without major economic reforms. The decision to have reforms advantage some while leaving others further behind was pure shitfuckery and Thatcher did everything as contentiously as possible.
Blair and Rudd strike me more as god botherers than Howard or Thatcher and the ALP have perpetuated and extended Howard's drive towards private religious education and service delivery. The ALP right has an equivalent group in the Libs. Its all the same here. Organised religion has an each-way bet on Australian politics and in 2 horse race they can never lose. The conservatives have had some obvious problems with religious branch stackings and people leaving in frustration and its arguable the party has shifted to its detriment. Labor and some unions have a complex history with organised religion. In some ways it might be symbiotic and reflective of membership but it can appear like cronyism.
As long as they don't call it footy its fine. Football is a broad term for a lot of codes.