If a billionaire’s approach to philanthropy is a reflection of himself, Charles Koch’s latest initiative tackling poverty embodies both the wealthy industrialist’s business acumen and his distaste for big government. The 3-year-old Stand Together Foundation has lately taken center stage in the Koch empire, which has been recalibrating some of its wide-ranging operation that is both villainized and revered by the American public. The shifting strategy comes as the GOP icon’s sprawling network of rich donors, powerful political groups and various tax-exempted advocacy organizations continues to downplay its more well-known but controversial political agenda, which has pumped hundreds of millions...