Kershaw's biography argues that Hitler, still a soldier, was transferred into Bavaria. Bavaria at that time had both a socialist government and a revolutionary movement with popular support among many soldiers. Soldiers also elected representatives, and they had official duties that connected to the socialist program of the government.

Kershaw suggests Hitler ended up as a representative (Vertrauensmann) of this regular army company, not as a member of any "Red Brigade". Kershaw says it's unclear whether he had any political sympathy for the socialist government. He may just have been trying to maintain his position in the military in a time and place where that meant working with a socialist government and elected soldiers' representative bodies.

It's not the same as being a member of the various "Red Armies" that existed on and off throughout Germany around this time, which were voluntary militias of socialist/communist workers and soldiers. Throughout the revolutionary period in Germany, soldiers often had the opportunity to elect representatives, and those representatives could be socialist or conservative. Kershaw quotes some witnesses claiming that Hitler supported the mainstream Social Democrats as a bulwark against the communists. This is compatible with Hitler being a pragmatic conservative faced with a perceived revolutionary threat, or with being a confused young man being influenced by very dynamic political processes. (Note that Germany's most conservative forces had made a temporary alliance with the Social Democrats to repress communism on a national scale at around this time.)

As Kershaw writes, on the dynamics of soldiers' politics in this time:

"If indeed, as was later alleged, he voiced support for the Social Democrats in preference to the Communists, it was presumably viewed as a choice of the lesser of two evils, or even, by those in Hitler’s unit who knew him of old, as an opportune adjustment betraying none of his real nationalist, pan-German sympathies. Ernst Schmidt, for example, who by then had been discharged but was still in regular touch with him, spoke later of Hitler’s ‘utter repugnance’ at the events in Munich. The nineteen votes cast for ‘Hittler’ on 16 April, electing him as the second company representative – the winner, Johann Blüml, received thirty-nine votes – on the Battalion Council, may well have been from those who saw him in this light."

So this means that many soldiers were conservative anti-Communists, and found that during the revolutionary events in Bavaria the best option they had was expressing support for Social Democracy. Hitler may have been elected as a soldiers' representative with the support of this conservative current among the soldiers.

Sources:

Kershaw's "Hitler: Hubris", ch. 4

Pierre Broué, "The German Revolution 1917-1923"