This is mostly true, but there were important exceptions that have repercussions to this day. I remember the founding convention of Labor for Peace. It was large and in many cases delegates represented their locals. I was in the Teamsters then and we had a sizable section of the union opposed to the war. My local 327 in Nashville was on record, as were a few dozen more throughout the country. The Missouri Teamster was outspoken against the war as was the Western conference. And a lot, certainly not anything like a majority, but a lot of the kids that refused the draft were working class kids. Many students had deferments.
Anyway as you get to know a lot of the middle level labor leaders of today, you find that a lot of them were active in the anti-war movement in their youth. I think these are some of the most important folks in the new directions in labor today. This has been my experience in steel, auto and mining in particular. I guess it's no accident that the ones who were most active in the rank and file movements of the 70's and 80's tended to have been against the war also.
Scott