It's way easier to understand when they just want to attack labor and absolve capital, it really is that simple for 99% of the discourse you read online.
The protections offered to unions goes far beyond standard freedom of association. Generally I think that is okay, but not in the case of public unions.
I think you may be misunderstanding. The right to join a union is the right to association. Right to association is not something provided by a union. In other words, you have a right to collectively bargain for certain working conditions and that is guaranteed by the 1st amendment.
both private companies and workers should not be allowed to band together to deny the government all contracts until they get the one they want.