Just because western Virginia voted to not leave the Union didn't mean there weren't Confederates from there. It used to be thought that there were about 7,000, mostly infantry ( enlistment records in Richmond were burned, so it's uncertain as to precisely how many). But recent estimates have boosted that to a possible 18,000. Which, balanced against the 32,000 who we know fought for the Union, shows western Virginia was indeed quite divided. Most of them joined the Virginia force organized under governor John Letcher. Some fought under General Henry Wise ( who'd also been governor), and there were also "irregulars", like MacNeil's Rangers.

If they survived the war( unlike Stonewall Jackson) ex-Confederates and their sympathizers were soon able to practice law and run for state elective office after the Flick Amendment of 1871 allowed them. Many did so, like Daniel Bedinger Lucas, the "poet laureate of the Lost Cause" who'd served under Wise. After the Flick Amendment the Unionist Republicans who had dominated the state were pretty quickly displaced by Democrats, many of them ex-Confederates, who then mostly controlled the WV government until the end of the century. When in the 1890's there was a general wave of monument-building to honor soldiers in the Civil War, there were therefore plenty of sympathetic ex-Confederates and their families within the state wanting Confederate monuments, and Democrats in power who were in favor of them being built.

By the 1890's, building the monuments was also pretty uncontroversial. The Lost Cause idea had been largely accepted that all the soldiers on both sides had been valiant, fighting for noble reasons. Maryland would even build one monument at Antietam Battlefield that commemorated both its Confederate and Union troops that had died there.