Oklahoma and other rural states owed a lot of their early left-leaning to the numerous attempts at a worker-farmer populist alliance through the late 1800's and the Progressive Era.

As explained by Professor Elizabeth Sanders in her book, Roots of Reform: Farmers, Workers and the American State 1877-1917,

In the Southwest, the growing impoverishment of farmers and the industrial-union organizing by the WFM and IWW engendered a growing radicalism that swelled the Socialist vote. After the decline of populism and then the Farmer's Union, many agrarian radicals in Oklahoma, Texas, Louisiana, Alabama and Missouri found a new home in the Socialist Party. The rise of large-scale timber operations, the western spread of the cotton economy, and the expansion of farm tenancy - the latter reaching 54 percent in the Southwest by 1910 - provided fertile ground for native socialism [...] like the Populists, Socialists were found disproportionately among single-crop producers in small, poor and isolated communities. Both movements were fed by the deep class resentments against landlords and bankers, lawyers and merchants in the towns. Within its most successful state (Oklahoma), the SP vote was correlated positively with rurality, tenancy and membership in fundamentalist churches and negatively with urbanization and the value of farm property (pg 61-62).

The book really is fascinating, and a key focus of early chapters is how the decline of agrarian populism by the early 1900's gave rise to Debs' Socialist Party. Most interesting is the fact that in socialist circles of the time, at least intellectual ones, appeal to farmers and agrarianism was absolutely off the table - Marxist theory held that farmers, as landowners, held the means of production and thus must be removed from said land - this was before strains of Socialism like Maoism seriously included farmers and poor peasants in the 'struggle,' as it is.

As described in the same book, Socialist Strength in states like Oklahoma was much more an outgrowth of the failure of the Populist movement, which failed to form an effective alliance of the 'producing classes,' i.e. urban factory laborers and rural farm workers, most notably those farm workers who had long been abused by landlords. The Socialist Party benefited from a deep tradition of agrarianism and even radicalism in rural areas, engendered by decades of abuse by the landowning classes, and essentially took the reigns of reformism and populism after the decline of the Knights of Labor. While the urban core of the Socialist Party emphasized more typical industrial Marxism, the Socialist Party in Oklahoma and other rural states were essentially fusions of the old Populist traditions and newer Socialist ideas and organizational principles.

What happened to the socialist party in these areas? First off, the Socialist Party central committee was very very resistant to adopting agrarian positions, due to the aforementioned Socialist Orthodoxy generally believing farmers to be a "class doomed to extinction." As described by Professor Sanders:

All mention of farmers was avoided in the first [SP] platform. For years, the most that official SP doctrine could offer farmers was government ownership of industry and transportation and the presumed advantages of collective farming over tenancy. After being fully proletarianized, they could become trade unionists and true Socialists (pg 63).

That isn't to say Southwestern Socialists didn't try to get the central party to adopt agrarian positions, the central party was just very resistant. More immediately relevant to SP decline, especially in Oklahoma, was the "Green Corn Rebellion," which took place in 1917:

Several hundred poor farmers plotted a people's uprising against the war [WW1]. They would march to Washington, gathering recruits along the way [...] the rebels managed to dynamite a few bridges and pipelines before being rounded up by local authorities. The organizers of the aborted uprising were convincted under the Espionage Act and sentenced to long prison terms. Although the Oklahoma SP had played no role in the affair (except to try to prevent it), thousands of Oklahoma Socialists were arrested in the aftermath. In a panic because Berger [a prominent SP politician and office holder, from Wisconsin] and the national SP executive committee were also on trial for their antiwar efforts, the state SP leadership decided to disband the Oklahoma Socialist Party in the hope of severing any connection between the national leaders and an actual antiwar conspiracy. Thus was the party's most dynamic state organization mortally wounded by prowar hysteria and then sacrificed for the national leadership (pg 69).

Also of note was the 'capturing' of the Democratic party, or perhaps vice versa, by the Populist party, exemplified by William Jenning Bryan's two runs for the Presidency and eventually the nomination, and election, of Woodrow Wilson to the Presidency -

The drop in presidential voting [for the SP] from 1912 to 1916 was surely related to the record of the first administration of Woodrow Wilson, when favorable legislation and appointments made the Democratic Party a more plausible reform vehicle for workers and farmers previously attracted to socialism. When Wilson campaigned as the peace candidate in 1916, the Socialist presidential vote, without Debs on its ticket, dropped from 900,369 to 589,924 (from 6 to 3 percent) (page 69).

Ultimately, the decline of the Oklahoma, and Southwestern, SP, is most often blamed on poor decisionmaking at both the state and national level, the preemption of reform by the Democratic party, the alienation of labor organizations and important intellectuals via SP opposition to WW1 and most prominently intraparty factionalism, thanks to aforementioned central SP resistance to agrarian positions, despite the strength of agrarian Socialist factions. As described by Sanders:

Among the proximate causes of the decline of socialism after it's 1912-14 peak, the most cited are the winner-take-all electoral system, the preemption of reform by the Democratic Party, the repression by local and national governments, the alienation of important labor and intellectual allies provoked by SP opposition to World War 1, and intraparty factionalism (pg 68).

Citation: Roots of Reform: Farmers, Workers and the American State 1877-1917 by Professor Elizabeth Sanders

Let me know if you have any other questions about the topic, or if you'd like me to go further in-depth into anything I've mentioned. The book really is fantastic for any one interested in American reformism, populism agrarianism and labor history, as someone with a major pertaining to these fields (Industrial Labor Relations) I can't recommend it enough.

Edit: Spelling, grammar

Edit 2: As pointed out by a commenter, my summation of SP decline forgets to mention open repression by local and national governments - it's my mistake for omitting that fact, I didn't want to lean too heavy into quotes, especially because the summation I paraphrased is more about national decline rather than just state. I've included the actual quote in the answer. Sorry for the error!

This is an interesting question and I think you can approach it from multiple angles. Oklahoma, and the US as a whole, heavily depended on agriculture in the early 20th century with 41% of the national workforce directly employed in agriculture. In Oklahoma there was a 'land rush' which started in April, 1889 after the passage of the Indian Appropriations Act which allowed white settlers access to two million acres of 'unassigned land' to establish homesteads. This led to a boom in small farms and sharecropping but these small farmers did not have the resources to properly farm the land they claimed. This was not an easy life, there was very minimal mechanization and no access to electricity. Everything was done manually and a drought could completely wipe you out or force you to mortgage your land. You can see from the 1910 Census excerpt for Oklahoma these farms were under 200 acres in size and were becoming increasingly mortgaged and there was an increase in the number of tenant farmers. So against this backdrop of across the Midwest and the Canadian Prairies you had the rise of various Populist movements such as the Farmers Alliance, Farmers Union and United Farmers (Canada). In Oklahoma, the Populists had waned in popularity by the turn of the century but the Socialists adopted many tenants of their platform and appealed to the growing population of indebted and tenant farmers.

With the rapid population growth, you also had the rise of the Baptist church. But this was not the same church you may be thinking about. Around this time was the rise of the Social Gospel movement and the Socialist Party of Oklahoma made use of messaging consistent with Social Gospel beliefs. Oklahoma preachers like Thomas W. Woodrow echoed Socialist beliefs in their sermons (or perhaps vice versa). This kind of cooperation between politics and religion did not just happen in agrarian Oklahoma, in the Prairie Provinces of Canada you had a similar marriage of a radical socialist farmers movement with Social Gospel; except in Canada they were much more successful and Tommy Douglas (an ordained Baptist Minister) would go on to lead the first socialist government in North America in the province of Saskatchewan. I mention Douglas as an aside and a possible 'what if' scenario for Oklahoma. But, the Socialist Party of Oklahoma opposed the entry of the USA into World War I, going as far as to organize an armed rebellion, the "Green Corn Rebellion" in opposition to the military draft. The Rebellion was put down with force and the Federal Government used it as a justification to crack down on the Socialist Party nationwide. That was the beginning of the end of the Socialist Party in Oklahoma. Between a forceful crackdown and the transition of Oklahoma's economy to one less based on agriculture, the Socialists never managed to recover.

Summing things up, you had the right circumstances for Socialism to prosper; rising inequality, indebtedness and demands for land redistribution, a Socialist party who understood their base well and had very effective messaging, and Evangelical Christian doctrine that was collectivist and not opposed to Socialism.

To what extent do we owe the Bank of North Dakota to these movements? It's one of the only state-owned banks in the U.S. from what I recall.

Might some of this explain why Girard, Kansas (not far from the Oklahoma border) was a socialist stronghold around the same time period?