It is not possible to be a member of significant minority, this would be a fallacy. But, I'm not as good as AI in explaining this and thus looked it up in Google:
While "significant minority" is
not an established logical fallacy, it can be used to commit two related fallacies: the appeal to minority and a flawed variation of the appeal to popularity (ad populum). This rhetorical tactic exploits the audience's biases by using the status of a group, rather than evidence, to argue for a claim