What the Union is saying is that they are entitled to people's money, and that people choosing not to be Union Members (and as such not paying dues) is a First Amendment violation. If I did not know better I would think this was an Onion story. By that logic the Union is violating my First Amendment rights by not giving me millions of dollars to buy television advertisements.
"Indiana's new right-to-work law should be struck down because it infringes upon unions' free speech rights by depriving them of the dues that fund their political speech, attorneys for a union challenging the law contend, citing the U.S. Supreme Court's so-called Citizens United ruling that eased restrictions on corporate campaign spending.
Attorneys for the International Union of Operating Engineers Local 150 argue in a court brief that Indiana's new law, which allows workers to not pay union dues even if a union bargains on their behalf, interferes with the union's free speech rights and "impinges on this fundamental right of union membership.""