your campaign assumes cis people can’t tell who’s cis and who’s trans. human adults can tell the difference between a natal male and a natal female with 99% accuracy (this is an inborn pattern recognition) and a pin won’t confuse the public into viewing a cis person as trans.
Okay so this is less for you, the kind of person who's wandered deep enough into the transphobic desert that you've started using terms like "natal male" and "natal female" when you already know the word cis because you used it early on, and more for people who have casually assumed that yeah, you probably can always tell who's trans: You cannot tell who is trans and who is not with anything close to a 99% accuracy rate.
That claim is a lie, and I don't know if you've been told it and accepted it as true uncritically, or you have just made it up yourself, but it is absolutely not true. Firstly, let's look at the information we have at telling apart male and female faces in cis people, which was studied as part of Bruce & Young's Face Perception (You mostly want chapter 3, here's a link): https://archive.org/details/faceperception0000bruc/page/104/mode/2up?q=sex
They concluded that we are remarkably good at telling the sex of a cis person's face, in that we get it correct about 95% of the time. That's not one error in 100, that's one error in 20. And that's when you remove hairstyles, makeup, and other gender cues that we all, cis or trans, deliberately adorn ourselves with. Then let's add to that the physical effects of transition that can occur- to start with, HRT changes how and where fat is stored on the body, which is a massive cue. Breast development in trans women and surgical removal of breasts in trans men provide another cue. Bone structure doesn't change as part of an HRT regimen, but facial feminization or masculinization surgery literally alters the facial bones. Laser hair removal for trans women and testosterone in trans men add or remove beard shadow even if the person in question goes clean shaven. Some things can't be changed, but almost every element that our brains use to correctly gender a person can be (and is, in practice) altered by trans people. This has an effect on how often you'll spot them. If I'm right, and if trans people are actually harder to spot than you might think, and given that trans people are like, what, maybe 1% of the population, what you end up with is the fact that if you're keeping an eye out for trans people and you identify 90% of us as trans (I am being spectacularly generous to you here- I do not believe the amount is even nearly that high) and you correctly identify, let's say, 98% of cis people as cis, and you challenge all the people you think are trans, then in a population of 1000 people you will have correctly spotted 9 trans people and misidentified 1, and correctly spotted 970 cis people and misidentified 20. You will have a pool of 29 people you accuse of being trans, and you will be wrong 2/3 of the time, and you will not even have "caught" all the trans people. If this were the case, and I'm right that trans people are harder to spot than you claimed, you would expect people who were really weird about this sort of thing to have made some pretty high profile mistakes, though, like claiming the pope was trans: https://www.pride.com/trans/pope-leo-xiv-transvestigation#rebelltitem8
Or claiming that the First Lady of France was trans: https://www.advocate.com/news/candace-owens-brigitte-macron-transgender
Or, and this is a personal favourite, claiming that trans personality Dylan Mulvaney is in fact DOUBLE TRANS having been forcibly transitioned as a young woman and then transtioning BACK AGAIN as an adult in a case of detransition masquerading as transition to give trans people a false sense of hope or something? When you get into the weeds on this it stops making sense because it's all cow shit: https://www.instagram.com/reel/DXwQo0VylMW/ All that said: sometimes, you can tell that an individual person is very probably trans; but that person also might have a hormone disorder, or be intersex or something, so even then you can't be SURE sure unless someone tells you. I'm one of these people, most of the time; I think most people clock that I'm trans, but I know for a fact and from experience that it's not all of them and it's not all the time (casually being asked by a nurse if you're up to date on your smear test does do wonders for a girl's understanding of whether or not she passes). The pin you refer to is from the chaff project, which can be found here, and the purpose of which is to encourage false positives (people thinking a cis person is trans) in order to provoke an understanding of how unworkable trans-exclusionary measures are in practice. SO in short: I assume cis people aren't as good at spotting trans people as you think. The science backs me up. Based on a history of who cis people accuse of being trans (cis women with short hair), yeah I absolutely think a pin badge with the trans flag on will bamboozle y'all even further. Hope this was a fun read, and if you sent this anonymous ask, please be less cowardly and get in touch directly. I'm more than happy to chat with you about trans liberation and how it liberates you, too, as a cis person.