A woman is promoting an animal rescue as a nonprofit on a social media platform, asking for donations, and telling people their donations are tax deductible. In reality, that is extremely questionable. How can it be confirmed she is nonprofit? If she is not, and is committing fraud, do we contact the IRS and/or the social media platform to shut her down? I searched the IRS site for nonprofits and her "business name(s)" are not listed.
Your best bet here is probably to contact the office that accepts charitable solicitation registration statements in your state, assuming that your state is one of the 39 states and the District of Columbia that has a registration requirement. The rescue doesn’t have to have 501(c)(3) charitable status from the IRS in order to have the obligation to register if it is making a “charitable appeal.” An animal rescue saying it is nonprofit and asking for money to help save animals probably constitutes a charitable appeal.
Unless it raises so little in contributions that it is exempt from registration because it isn’t worth the state’s time to be bothered with it, it probably has to register to solicit. A successful organization, or one that pays someone to solicit as part of their job probably has no exemption from registration. The state Attorney General and the charitable solicitation registration office have an interest in curbing illegal solicitations (and adding to their registration fee receipts), and would have the power to take legal action if she should be registered and isn’t. They are more likely to care than the IRS or the social media platform. If you find that she is registered properly, you will have answered your question (though perhaps not in the way you wish), and none of you would have reason to take any action so long as there isn’t any material misrepresentation on her site. If she isn’t properly registered, the state can take action against her.
If you are in one of the jurisdictions that doesn’t require registration, you may still be able to pursue the question in another state that has a requirement and where you know she does solicit. The foreign state may have less interest than her home state, and you may have a greater burden of showing she is soliciting there, but most states are happy to add to their registration lists.