Freedom From Union Violence Act of 2014 - Amends the Hobbs Act to exempt from provisions that prohibit obstructing, delaying, or affecting commerce or the movement of any article or commodity in commerce by robbery or extortion and threatening physical violence to any person or property in furtherance of a plan or purpose to interfere with commerce by threats or violence, any conduct that: (1) is incidental to otherwise peaceful picketing during the course of a labor dispute; (2) consists solely of minor bodily injury, or minor damage to property, or threat or fear of such minor injury or damage; and (3) is not part of a pattern of violent conduct or of coordinated violent activity. Subjects such conduct to prosecution only by the appropriate state and local authorities.