It would not be accurate to label the play as political propaganda. Shakespeare certainly raises serious issues about political leadership and governance, which are pertinent issues in any age and country and were particularly sensitive in the time and place in which this play was written, with Queen Elizabeth I nearing the end of a long reign without any obvious heir. But while the play stimulates discussion of such topics it does not make any firm statements or draw conclusions, as a piece of propaganda would do.
The question of whether Shakespeare did intend this work as propaganda does sometimes arise, however. For instance, some critics have seen it as arguing against one-man rule and in favour of a republic, as Caesar, the man aspiring to kingship very often appears as an unattractive self-aggrandising character, while the chief of the conspirators against him, Brutus, is portrayed as a noble individual motivated by high ideals. But Brutus also has his faults, being naive and perhaps too convinced of his own self-worth, while the rest of the conspirators don't appear very honourable (although Cassius has certain positive qualities). Even less appealing are the people of Rome in whose interests Brutus purports to act; they appear as a rowdy and unthinking mob.
The play, then, aims to do full justice to the complexities of the situation. It resists easy judgements and refuses to provide clear-cut answers. This makes it the very opposite of propaganda. Instead, it focusses on the all-too human traits of the chief players in a momentous political drama. It explores the tragic dilemma of an idealistic man as well as exposing the raw, cynical nature of power-politics and the sheer brutality of war, vividly conjured up in a soliloquy by Antony:
A curse shall light upon the limbs of men;
Domestic fury and fierce civil strife
Shall cumber all the parts of Italy (III.i.262-264)
In a word, the play deals with real life, which seldom provides straightforward solutions, and does not attempt to go beyond this to impose judgements and conclusions of its own.