Yesterday, a judge ruled that it was illegal for the government to force a mask mandate on anyone. Would that not apply to private healthcare providers?

The government cannot force anyone to wear a mask nor can they force anyone to not wear a mask. This is up to the choice of the treating physician and what they are willing to do.

See: 8:21-cv-01693-KKM-AEP in the United States District Court Middle District of Florida - Tampa Division

https://s3.documentcloud.org/documents/21636220/047124235804.pdf

Government entities cannot force someone to give up their own rights to treat a patient. Similarly in, Masterpiece Cakeshop v. Colorado Civil Rights Commission, the Supreme Court rules that a government entity cannot violate the rights of the seller to protect the rights of the purchaser.