In the wake of the October Revolution, how was the military culture of the former Russian Empire transformed? Was there an effort to organize military forces in accordance to egalitarian and humanist socialist principles? What discussions were had about how the role of the military would change under socialism?
Essentially, how red was the Red Army?
Someone with more expertise in this area might be able to give a more comprehensive answer, but I just recently came across information in my research that may shed some light on your question.
The book I'm reading is focused on the region of the Caucasus (particularly Chechnya, but the surrounding areas are discussed rather in depth as well). The Caucasus was conquered in part of the Tsarist regime's conquests in the second half of the 19th century and was rather firmly under Russian control at the time of the Bolshevik revolution. In discussing the revolution, the author makes this interesting point about the ensuing civil war:
The Bolsheviks described this war in a simplified, simplistic way as being between “revolutionaries” and “counter-revolutionaries” or, in a more widely accepted terminology, “Reds” against “Whites.” This description became dogma in Soviet historiography and was fairly widespread even in the West. But things were not so simple or straightforward. In fact, these three or four years were among the most – if not the most – chaotic in Russian history. A huge number of participants in ever-changing coalitions were involved in what amounted to a war of all against all. Ideological, political and social struggles on every conceivable level, from the entire country to a single village, were intertwined with religious, national and ethnic conflicts becoming more complex with the intervention of foreign powers. And to complicate the matter further, almost every single participant in the civil war at some time experienced an internal, often armed struggle within its own ranks. (119)
This is illustrated in what was going on in the Caucasian region at the time. With the Tsarist regime toppled, the "mountain peoples" briefly declared independence (after all, some 150-ish years of Imperial Russian troops invading their land, burning down their villages and slaughtering or subjugating their people didn't really make them eager to stay a part of Russia when push came to shove). Originally the plan was to form a "Western-type secular democracy"(121). However, that dream was quickly quashed when a White army rode in and conquered their main cities, demanding they stay loyal to the Russian empire. This put them in the position to consider siding with the Bolsheviks, who rather cleverly promised the Muslim Caucasians a more or less autonomous government under the new order with more religious freedom than they had been allowed under the Tsar (apparently the selling slogan was "Shari'a and freedom"). The problem was once the Bolsheviks won out, they reneged pretty much entirely on all of their promises and the Caucasians were once again left in a state of oppression.
Anyway, the point is that at least at the outset, it wasn't that the Russian army reformed its outlook and policies, it's that the population splintered so dramatically along ideological lines and were all fighting each other (to say nothing of the intervention of foreign troops like the Ottomans creeping up from the south) until eventually the Bolsheviks were able to consolidate power.
I hope this helps! I'm not too well-versed in the Russian military itself and how it may have altered its tactics once the Bolsheviks were in power, so I'll leave that to someone more capable. I'd be interested in knowing the answer, too.