The Republican state was a coalition of various factions. Anarchists (CNT-FAI), Non-stalinist Communits (POUM), Soviet Style Communists (PCE), Socialists (PSOE), and republicans (IR and UR). The Spanish Civil War was a civil war within a civil war. Quite a mouthful.

The Republic was in a Civil War with Fascism. Within the Republic Anarchists and Communists conducted a revolution. This early period is noted in detail by Orwell in his Homage to Catalonia (A great read, and you should read it if you would like to see a first hand account in the anarchist militia lines.) Women were gaining rights and standing with an egalitarian mindset usurping the conservative nature of Spain. The formal "you" in Spain was dropped for the informal. Comrade was part of everyday vernacular, and "don" became a word of humor rather than one dignifying respect. During the middle and end of the war the Republic under the continually influential hand of the soviet union purged the POUM, and CNT-FAI militias.

The Soviet Union supported the Spanish Civil War to be a bulwark against fascism. The Soviet Union supported the Republic not to directly form it into a communist nation, but to maintain a republic that would be an ally in what ended up being WWII. Stalin wanted one socialist state, and directly supporting a second communist nation risked the threat of a fascist and capitalist coalition again them. The soviets were the largest supplier of arms and supplies to the Republic. The government purposefully neglected to fully supply militias. The Soviet Union bolstered the PCE and aided the formation of a true Republican Army instead of an assortment of militias. Officers were PCE members and any influential position was held by a communist. As you can see, they had qualms aiding the anarchists and after gaining enough influence, did their best to stifle anarchist and non-Stalinist communists goals.

The Spanish Civil War - Hugh Thomas

Battle for Spain - Anthony Beevor

Homage to Catalonia - George Orwell