You act as though anti-union FUD can't affect members. That's kind of ridiculous... if it didn't affect MEMBERS as well as non-members, what would be the point?
If I'm a less-educated union member who has no concept of what life was like before unions, and constantly hear that unions just take my money while providing no benefit, I'm probably likely to be swayed. What's the union going to do? Tell me about how 50 years ago companies would literally put my life at risk because there was no downside for them. And then the people financing the anti-union movement are spewing "Well that was 50 years ago, that would NEVER happen again" - all while doing everything they can to drive up hours, drive down safety, and insulate themselves from any responsibility RE: workman's comp.
For the average joe who just wants to go to work and get a paycheck, the bigger picture is often lost.