The early Red Army had a lot of units raised from diverse origins, and many were extremely revolutionary in politics – such as Red Guards, railway workers, ex-partisans – and often centred around a charismatic leader. These units tended to have an ethos at odds with the regular Red Army that Trotsky was building. They favoured a very personal sort of command, wanted to preserve elements of irregular warfare, disliked operating in a formal system and were intensely suspicious of military specialists. This came to be labeled partizanshchina.
There was an intense battle to stamp out these tendencies, because they were frequently the source of considerable difficulty for the Soviet war effort. The Czechoslovak Legion made such easy progress in part because their opponents would not obey orders reliably, and would often halt to discuss political issues.
In extreme cases, where the problem stemmed from the ambition of a leader, it was often termed atamanshchina. In the early days whole armies aligned with the Reds might go rogue with their "ataman". Gregoriev in the Ukraine was a particularly awkward case for the Soviets. The North Caucasus in 1918 even saw competing commanders arrange trials, and order the death sentence on each other.
Progress was made rapidly though. Commanders with too close a connection to "their" units were relieved of command or sent to other fronts. Political workers and commissars stopped the practice of unsupervised political meetings, so non-orthodox Bolshevik opinions were unable to prosper.
The issue of using former Tsarist officers was fraught, but most commanders realised that the voenspetsy were an asset, even if they disliked them politically.
It broke down, however, when commanders were able to operate away from central control, and especially if they had good political support. Stalin's "Tsaritsyn Gang" always operated as a law unto themselves, and eventually their refusal to obey orders was a major cause of the disaster in the 1920 Polish campaign. Likewise, Chapayev, isolated out in the Urals, was able to operate very unprofessionally – until it cost him his life.
The political version of this position was called the "military opposition". It came to a head at early congresses in 1918, but Lenin and Trotsky stood firm and the principles of central command, regular war, professionalism and the appointment of ex-Tsarist officers remained.
Nevertheless, many old revolutionaries remained opposed to a professional army on ideological grounds and if they were sufficiently far from Moscow, they often supported those commanders who adhered to the former Bolshevik orthodoxy.
They was brought to heel in many of the same ways as the partizanshchina. Proponents were separated and sent to the front (where they often saw first hand the unfortunate effects of their position). They were denied room to promote their views. And so, finally, the success of the new army won most of them over.
Initially the Soviets suffered the worst from partizanshchina, because they had worked tirelessly to promote it up to the October Revolution. Unsurprisingly, at first their followers took them at their word.
But it was present in all the armies, because they too had arisen from similar origins, often with units forming around charismatic leaders. The Poles, Latvians and Estonians got a handle on it early, and rapidly professionalised. The UNR never did, which is one reason it was so weak militarily.
The main White armies though suffered from it badly right up to the end. Atamans like Bulak-Bulakhovich, Shkuro and Annenkov would have been relieved of command, by force if need be, if they had been Soviet. One of the causes for the White failure was the indiscipline of senior officers, who treated their units as their personal army, and who broke army policy on political issues.
This is one area where the Red Army was considerably better than its White opponents, and a significant reason why they went on to win the civil war.
Leon Trotsky, My Life
Especially Chapter 36, on the "Military Opposition".