AT&T Inc.’s practice of exempting its streaming video services from data-usage caps is rankling competitors and shaping up as a major issue for regulators set to weigh the telecom giant’s proposed $85.4 billion acquisition of Time Warner Inc.

When AT&T rolls out its $35-a-month DirecTV Now online TV service this month, its wireless subscribers will be able to stream as much as they want without it counting toward their monthly data caps. But if the same customers binge on outside services like Netflix or Hulu, those bits...