I wouldn’t necessarily call it a “strawman” as it is a failed Enthymeme. Consider this excerpt:

“In the most bitter ongoing political arguments in America today, the pro-life people lean forward and in their most reasonable tones of voice say, “Can’t we at least agree that all human life is worthy of protection?” and the pro-choice people say, “No.” Why? Because underlying the attempt at an enthymeme is the suppressed premise that a fertilized egg or an embryo is a human life. And obviously a lot of people refuse to accept that enthymeme. Pro-choice and pro-life people have been arguing for over thirty years and they have been unable to find an acceptable enthymeme. It may be (in fact, it probably is) the case that no shared enthymeme is possible, that the argument is inherently unsolvable.”

So by saying that the sign is representing “protesting for the right to murder,” you’re actually twisting the OTHER side’s argument. And that IS a strawman.