A state or region's devotion to the Confederate cause was usually linked to the percentage of the white population who were slaveholders. This varied depending on the soil conditions: areas suitable for large-scale plantation agriculture such as the Mississippi Delta, the Alabama-Georgia Black Belt, or the South Carolina coast featured gigantic plantations with thousands of people enslaved on them. The slaveholders here were some of the richest men in the United States, and their wealth was entirely tied to slavery. Regions with poorer soil, or mountainous regions such as the Appalachians could not support large plantations and thus the rate of slave-holding was lower, and among those slaveholders the average number of slaves per slave-holding household was smaller. White farmers in these marginal regions were poorer than their plantation-owning counterparts, and among those who did have slaves, a smaller percentage of their wealth was tied to the institution vs. a plantation owner. Most of the famous episodes of anti-Confederate armed resistance occurred in these marginal regions.

This map shows the percentage of the county population in 1860 who were enslaved: https://www.loc.gov/resource/g3861e.cw0013200/?r=0.388,0.246,0.458,0.199,0

As you can see, the Appalachian counties have a smaller number of slaves, and as an example, people in what is now West Virginia did not feel a compelling reason to join the rest of their state in seceding, so West Virginia broke away in 1861 and supported the Union.

Newton Knight, the anti-Confederate resister who the movie was based on was from Jones County, Mississippi, which had one of the lowest slave-holding rates in the state. Jones County is part of the Southern pine belt region which stretches across several states, with poor sandy soil that couldn't support plantation agriculture. I don't have the figures for Jones county handy right now, but for next-door Covington county, in 1860 half of the slave-owning households owned only 1-4 slaves, and 71% of all Covington County slaveholding households owned fewer than 10 slaves. Farmers in Covington were poorer than average, the median value of a Covington County farm in 1860 was $1,234, far below the state median of $5,155. So clearly, in the region Knight was from, white people were poorer and less economically-dependent on slavery (even if they still benefited from other aspects of the white-supremacist hierarchy). If you look into the data from census records, this pattern of smaller slave-holding and poorer farms would hold across the pine belt and Appalachian regions, where many of the Southern unionists came from.

Knight joined the Confederate Army like many other men from his area, but later deserted and started fighting against the local Confederate troops in 1863. Many people like Knight were disillusioned by the passage of the 2nd Confederate Conscription Act in 1862 which included an exemption for men who owned more than 20 slaves. The richest who had the greatest interest in preserving slavery were exempt from the draft, while men such as Knight and other non-slaveholders or small slaveholders from poorer regions were still being drafted. This combined with the Confederate defeat at Vicksburg in 1863 led to a surge of desertions from the Confederate army, many of the members of Knight's band were deserters who joined at this time. Others across the South just went home and passively resisted by not rejoining the Army.

So while each person had his own convictions, it generally came down to economics and how tied a community was to large-scale slavery.

References: Bynum, Victoria. (2003) The Free State of Jones: Mississippi’s Longest Civil War. University of North Carolina Press.

1860 United States Census