Threatening to Fire Someone for Signing an Initiative or Referendum Petition = Improper Influence on a “Voter”?

State statutes in Maine, New Hampshire, and Utah ban “improper influence” on “voters.” Each provides, with immaterial variations, that,

A person is guilty of improper influence if he … [t]hreatens any harm to a public servant, party official or voter with the purpose of influencing his action, decision, opinion, recommendation, nomination, vote or other exercise of discretion….

“Harm” means any disadvantage or injury, pecuniary or otherwise, including disadvantage or injury to any other person or entity in whose welfare the public servant, party official or voter is interested.

Both states’ laws define “voter” as, essentially, a person who is “registered to vote.”

My questions: Maine and Utah have the initiative and referendum. Should these statutes be viewed as barring employer threats to fire someone for signing an initiative or referendum petition, on the theory that the signers are acting in their capacity as “voter[s]” engaged in “action, decision, … or other exercise of discretion”? Or should those provisions be read as limited to threats aimed at influencing how a voter votes in the election itself?

Note that Utah law states that, “A Utah voter may sign an initiative petition if the voter is a legal voter,” which makes it sound like signing an initiative petition is a task of a person acting as “voter.” Maine law likewise says, “A person circulating a petition must provide the voter the opportunity to read the proposed direct initiative summary and fiscal impact statement required by section 901 prior to that voter signing the petition.”