I'd call the store ahead of time

This isn't a bad idea. It's a courteous gesture that can help avoid problems. But the law doesn't require it. As the woman says she hasn't had issues at other stores. Notice and manners or not, the onus is on the store to provide reasonable accommodation.

she's an attention seeking bitch.

Perhaps. Perhaps also the store employee and the police are that as well and beyond. The police claim she took a swing at them but this is not on video. There is a picture of the police on top of her outside of the store.

Absent proof or evidence of her condition, the business had every right to refuse her and ask her to leave.

This is what I found about the law as interpreted by the NB Human Rights Commission (BTW human rights tribunals are not final decisions and can have their decisions be over ruled in civil court):

"The New Brunswick Human Rights Act does not prevent service providers from requiring patrons to wear a face mask. However, should a patron be unable to wear a face mask due to a mental or physical disability, the patron has a duty to inform the service provider of their inability to do so. Once the service provider is advised of same, the service provider has a duty to accommodate to the point of undue hardship.

If a service provider, however, requires medical documentation to support that the patron cannot wear a mask due to a mental or physical disability, the patron needs to provide it. The medical documentation would need to set out that for medical reasons, the patron is unable to wear a community face mask or any other type of mask. The service provider’s duty to accommodate would be on hold until such documentation has been provided. Requests for medical documentation beyond this may not suspend the service provider’s duty to accommodate until it has been provided.

Even though the patron cannot wear a mask for medical reasons, they must continue to follow recommendations from the New Brunswick Chief Medical Officer such as following physical distancing rules, coughing into their sleeve, hand washing, etc."

I'm unsure of the NB HRC's interpretation of a service provider requiring medical documentation, if this applies to any service provider or only to service providers that in providing their service would normally require medical documentation. On the face of it it looks like you are correct that in NB proof of exemption is required.