The slogan does not make me anxious. I know what it "really" means, and as I stated previously I am 100% in support of that message. I am frustrated because I believe there are better ways to communicate it to people in a way that is generally more persuasive.
I don't think it "hypothetically" harms the cause, I believe that it does. I only need speak to my more traditional extended family members, who will read slogans like this and react in a negative way, even though I know they could be convinced otherwise. Does it suck that they can't "read behind the lines" with slogans like this? Yeah. But public messaging is hard, and just amplifying existing messages won't solve that problem.
Lastly, "I'm not sure that it's possible to come up with a slogan that isn't read badly by opponents" seems like kind of a cop-out. Of course it's impossible to say something someone will take issue with. Communicating messages isn't an all-or-nothing game, what I am saying is I think people need to do a better job changing minds than they are now.