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fiscal conservatism which wants to deregulate and remove "red tape" from businesses such as equal opportunities laws
To me, the word "fiscal" has a really specific meaning, i.e. tax and spend. Therefore I would say that measures to do with regulation don't really have a fiscal dimension? Maybe I'm splitting hairs though. If you were to say laissez-faire then I would agree with you.
But don't forget the situations where deregulation is the progressive position (i.e. anti-trans / choice laws).
After he contradicted himself in his first paragraph I kind of lost interest. If you accept that governmentally-enforced regulation can foster social progress then I don't see why supporting such regulation (or deregulation) cannot in and of itself be described as progressive.