It occurs to me that Phil Ochs got a few swipes in at the unions (though aimed from the left, not the right). In Love Me I'm A Liberal:

I cheered when Humphrey was chosen
My faith in the system restored
I'm glad the commies were thrown out
Of the A.F.L. C.I.O. board
I love Puerto Ricans and Negros
As long as they don't move next door
So love me, love me, love me, I'm a liberal

Also in I Ain't A-Marching Any More:

Now the labor leader's screamin' when they close the missile plants,
United Fruit screams at the Cuban shore,
Call it "Peace" or call it "Treason,"
Call it "Love" or call it "Reason,"
But I ain't marchin' any more.

And the whole point of Links On The Chain was to citicize the unions (for not being radical enough). After going over the early, heroic history of unions, he goes

And then in 1954, decisions finally made
The Black man was a-risin'fast, and racin' from the shade
And your union took no stand, and your union was betrayed
As you lost yourself a link on the chain, on the chain
As you lost yourself a link on the chain.

[two verses omitted here]

And the man that tries to tell you that they'll take your job away
He's the same man that was scabbin' hard just the other day
And your union's not a union til he's thrown out of the way
And he's chokin'on your links of the chain, of the chain
And he's chokin' on your links of the chain.

For now the times are tellin' you the times are rollin' on
And you're fighting for the same thing, the jobs that will be gone
Now its only fair to ask you, boys, which side are you on?
As you're buildin' all your links on the chain, on the chain
As you're buildin' all your links on the chain.