BOGOTÁ, Colombia—Venezuela’s political opposition welcomed funds from private donors and foreign governments as the movement to remove authoritarian leader Nicolás Maduro gained momentum earlier this year, with money earmarked to help hundreds of Venezuelan soldiers who defected to neighboring Colombia.

But now, accusations that two opposition activists pilfered tens of thousands of dollars from those funds are threatening to become an embarrassment for a coalition that is heavily dependent on the largess of dozens of countries,...