This is only necessarily true in a closed ship environment. In right to work states where "closed shops" are not allowed union and non union workers can work side by side with their own wages and benefits.
I have worked in a mixed shop before. I was not a union member and I did not receive any of the union benefits. The fella that worked the same exact job right next to me who was a union member made $3 more per hour, had 2x as many breaks, received a better health care package and had more sick time off.