[Just another Joe]

"This bill is telling me to shut my mouth," said Maureen Dinnen, president of the teachers union, who was visibly shaking with anger after the vote.

From what I read it's not telling her to shut her mouth, it's telling her to not use dues money to back any political candidate.
Not all the people paying dues want to back the same candidate.

[mongrel]

It's also telling her she can't force teachers who disagree with her politically to fund her mouth. So basically she's the one advocating the repression of free speech. She's arguing for the state to allow her to have compulsory funding of her speech.