"It has also circulated in Iowa and Michigan."

You can say that again! And the Michigan situation illustrates your point very well. I wrote about the problem months ago when the co-chair of Michigan's Republican Party posted to her Facebook page that Michigan residents needed to do something about a particular school district that supposedly allows "furry-identified" students to use litter boxes in school.

Quite the brouhaha ensued as the (very Republican) school district superintendent issued an astonished press release to say that, obviously, the rumors were untrue. He chastised the Republican Party co-chair for making him issue such a ridiculous press release. He suggested that if anyone were concerned about litter boxes, they should talk to school administrators before spreading ridiculous, wholly untruthful rumors.

Did that stop the rumors?

Not at all.

As for the Republican Party co-chair, who at this point knows for a certain fact that her claim was untruthful ... well, it's instructive to know that she never made a public statement and that she never took that post down from her Facebook page.

It's still there. Right now. Gullible Republican voters are still reacting to it as if it were true.

Take that for what you will with respect to Republican Party leadership and respect for the truth.