While "Right and Left" are not meaningless terms, their meaning varies from place to place, time to time, and the mind of the speaker. A Right/Left taxonomy seeks to cram diverse multi-dimensional societal arrangements into a one dimensional line, suitable for polemics and propaganda but not for useful categorization, thought or analysis. That is especially evident in this context.
Considering we have not just human but many other species as well, individualism vs. collectivisim is very apt. It clears away the anthromorphism of a lot of terrestial political terms and boils things down to fundamentals that would apply to most, if not all, sentient aliens.
The collectivism/individualism spectrum has real substance for humans, since it addresses the rather fundamental and both philosophical and highly practical question of "who owns you?" I.e., who is entitled to control, exploit, and dispose of you and the fruits of your efforts for their purposes? Do you own yourself? Do one or more other people own you (could be a congress, commissar, corporation, commissioner, king, the electorate of a direct democracy or some other group who are the "state")? That is the first question.
Then there is the issue of whether this ownership is total, partial or qualified, and whether you can rent yourself back by some means, such as performance of corvee labor or other feudal or regulatory requirements, military or other compulsory service, payment of taxes, etc.
This question is fundamental for humans, who can be solitary but are naturally gregarious and cooperative for mutual advantage. The question may be of little relevance for other species with different biology. For a solitary species that may associate only for mating when under a biological imperative (something beyond Fanatic Individualists), the question does not arise, but then one would not expect them to be able to or seek to organize space empires.
The situation changes where the individual organisms are are symbiotes or otherwise biologically incapable of surviving alone. In the extreme case of the empire ruled by an alien Hive Mind's empire, the controlling intelligence is entitled to dispose of all hive members, whose design and only purpose is to be of use to the Hive Mind. They live to serve as organs of the Hive Mind. As mentioned above, cradle-to-grave arrangements for their welfare might be prudent to maximize their usefulness in some cases, while setting them to hazardous tasks or disposing of them for military purposes might be a wise choice by the Hive Mind when their useful service life comes to an end or they malfunction.
Allowed forms of government depend on who the government are and other aspects of ethos, biology, culture etc., and the quest for simplicity often involves some rough corners.
