I think that the most basic idea from the plays help to bring out the connection to Nazism. Consider the idea of the transformation into another form, along with abdication of previously held values as being symbolic of Nazism. In a setting where individuals believed so many different and divergent thoughts, the conformist approach of Nazism blanketed so many people that the ideological change was fairly shocking. At the same time, the form in which people change, the rhinoceros, is a form where brute force and destruction seem to result. This is another Nazist reference in reflecting how the result of transformation is not necessarily one that embraces the subtleties of difference and tolerance. The idea that Berenger struggles to be the lone voice of humanity when all else capitulate to conformity also brings to light the idea of how individual human beings had to fare in countering the force of Nazism. There is much from Ionesco's own life in this theme, as he watched former colleagues join fascist movements. In the embrace of these ideologies, they forsake all they believed before and within this, there is much in shock of such a change. This was representative of much in Europe at the time of the rise of the Nazis:
In conforming to the rhinos’ ideology, the townspeople become themselves savage creatures. They lose their humanity, their individuality, their sense of self. Their identities, completely reshaped by their adherence to rhino values, are transformed by their desire to go along with the herd, to be just like everyone else, and to play it safe. The extent to which all the characters in the play, with the notable exception of Berenger, collaborate with the rhinoceroses makes them, in the end, no better than the thick-skinned beasts. In fact, the people become rhinos.
This ends up becoming a powerful statement about the Nazis and their influence at the time of their ascension into power.