Below is a link to a document that federal workers might find helpful in contesting President Biden’s vaccine mandate if they determine that information applies to them. While I have written the document to address President Biden’s order specifically, it contains legal and factual arguments that non-government workers can make if the information applies to their situation. Keep in mind that the Constitution is only a limit on government action. But the Constitution can limit a private company if it acts as a government agent. President Biden has mandated that employers who have 100 or more workers must require those workers to be vaccinated. A private employer of 15 or more employees cannot discriminate against someone based on race, color, religion, sex, or national origin. Such discrimination would violate Title VII of the Civil Rights Act. Thus, Title VII of the Civil Rights Act should protect a person’s exercise during private employment of his sincere religious belief not to be vaccinated. Incidentally, Title VII of the Civil Rights Act also protects federal workers from religious discrimination. There also could potentially be a claim brought by an unvaccinated person under the Americans with Disabilities Act (ADA). I have cited the authority for each point in the endnotes. You can thus assess for yourself the weight of the evidence and the validity of the legal arguments.
Below is a helpful brocure from First Liberty Institute.