We can´t ignore the fact that the regimes share knowledge and tactics. they see what goes nice and what doesn't engage in which country, and apply accordly.
A defining trait of fascism is positioning itself as a defender of the society’s noble, threatened heritage, including traditional religion, against those outside forces that would disempower the (actually powerful) in-group. This helps distinguish it from other forms of totalitarianism.
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One provides the moral rationalisation for the other. They can't do without each other.