That's not egalitarianism that is Anti Conservatism, anything relating to National Renewal and 'Changing of the old guard' is typical of a fascist ideologue. This is also seen in Italy during the build up to war and particularly after Abyssinia and in Japan to a limited extent. The fact that you used as evidence, that they promoted members of the party, members of the SS and ultra-nationalist radicals, shows that its not egalitarianism at all but motivated by a wholly different factor.
Also simply having a labour union doesn't make them socialist, the purpose of the union is what makes it socialist. The mandated unions of Fascist regimes were not used to protect workers right or as a security for workers, they were used as a form of control over both industry and the workforce by the regime in order to penalise both for anything which was not in the 'national interest' (e.g. high productivity low cost).
Simply because fascist ideology shared some elements with socialist thought does not make them Socialists.
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