Were there Mensheviks who fought on the side of the White Army during the Russian Civil War?

Cheers to /u/OldWorldGlory for the summons.

In the first place, we need to be wary of being too prescriptive with labels. The Russian Civil War saw a bewildering array of local and national forces locked in a very fluid political environment. It was, as we'll see, perfectly possible for individuals to move between parties and factions in the space of a few years or even months. The best way to view the 'Reds' and 'Whites' is as shifting and rather nebulous coalitions, rather than cast-iron factions.

This was particularly true of the Mensheviks. Unlike the Bolsheviks, the Menshevik wing of the RSDLP had essentially splintered by 1917, with three informal factions emerging - Martov's Internationalists, Tsereteli's Right Mensheviks and Plekenhov's Unity group. The specifics of each group aren't particularly relevant to this discussion but broadly they can be seen as ranging from left to right, respectively.

Like the Socialist Revolutionaries (SRs) the Mehsheviks went into a period of deep internal debate after October 1917 and the January 1918 disbandment of the Constituent Assembly. At its heart this debate questioned what the approach should be to the new Soviet government. Unlike the Right SRs, the Mensehviks were still wedded to the soviets as institutions (ie they did not reject 'Soviet power' per se, just the Bolshevik monopoly on it) and were aware that a repudiation of this would essentially pit them against the Russian working class.

But while the immediate task of the Mensheviks was to try and win power back from within the the Soviet movement, the advent of Civil War made this untenable. Their process that year came to naught as the Bolsheviks pulled down the shutters on opposition groups in the struggle against the Whites. With some exceptions, below, those individual Mensheviks who didn't pass into exile generally chose to reluctantly support the Soviets. The nebulous boundaries of Russian Social Democracy made it easy to either formally join the Bolsheviks or work within Soviet institutions as a Menshevik.

So no, the Menshevik party did not generally support the White armies or anti-Soviet factions. When the Right SRs convened the Komuch government in Samara, holding that legitimate authority derived from the Constituent Assembly rather than the soviets, the Mensheviks generally kept their distance. Some individual and lower party organs did cooperate with Komuch but this ended once Kolchak installed an anti-democratic regime in Nov 1918.

(Similarly Georgia was a Menshevik stronghold that remained neutral-ish until 1921 but was never aligned to the White movement.)

So generally the Mensheviks wavered and splintered but never openly opposed the Soviet movement. They were caught in the middle - anti-Bolshevik but not anti-Soviet. This left little ground for cooperation with even the mildest armed insurrections against the Bolsheviks (ie Komuch).

But you will always find individual exceptions. One of the most notable, and illustrative of the period's fluidity, is Ivan Maiskii. He was a pre-war Menshevik who in 1918 joined the Komuch government as Director for Labour. For openly joining an anti-Soviet movement Maiskii was expelled from the Mensheviks. After Komuch's dismantling by Kolchak, Maiskii joined the Bolsheviks and built a career as a diplomat, becoming ambassador to Britain in 1932. He survived Stalin and died in 1975.

Sources

This is all fairly general. Swain's Origins of the Russian Civil War is a decent place to start reading.