The list of Itaian fascist mathematicians is, unfortunately, quite long, given that fascism lasted for 20 years and it was basically impossible to get a relevant position in accademia without supporting the regime (some professors resigned when it was imposed to swore loyalty to fascism to every University professor).
It is not easy to distinguish between those that were sincerely fascist and those that merely adopted a comfortable neutrality, or simply faked loyalty to fascism being intimately at fight with it.
Surely Francesco Severi was strongly supporting fascism and you can find a reasonably detailed description of his positions in here: paper by Goodstein and - AMS Babbitt, together with references therein.
Surely a devoted fascist was Luigi Fantappié; its famously recorded in André Weil autobiography an episod in which he went to Volterra (who was a Jew) to convince him of how beautiful the Italian new Law against Jews was. The Law eventually determined that both Volterra and Levi Civita were permanently thrown out of Italian University. Also he was appointed for some years as a Professor at University of Sao Paulo, Brasil, and he gave conferences throughout Brasil which were intented to promote fascism in that country.
Enrico Bompiani and Mauro Picone were two others very relevant nathematicians that completely sided on the fascist side from the very beginning, and gained powerful poisition in the academic environment through this.
A brief but informative summary of this development may be found in Benzi's slides and in this work about the Italian Mathematica Union UMI (paper by Giacardi and Tazzioli)