Not necessarily. The Constitution only applies when there is governmental action. Even if the OSHA mandate is struck down, nothing in federal law is going to prevent people and businesses from maintaining their own private mandates (subject to law and contract). Google, Amazon and other woke companies are going to continue their own mandates. The OSHA mandate falling will prevent the government from forcing this on all businesses regardless of what they want to do but businesses can still put into place mandates subject only to federal and State law. The EEOC process is the federal guideline. States have other protections as well, but these vary widely.
Federal law does require religious accommodations and ADA accommodations. The liberty counsel website does a good job of outlining the procedures in place.
A friend of mine works for a private company (I also used to work there) that has FedGov contracts. This private company is fairly conservative but the FedGov threatened to pull the contracts or at least not renew them if the private company did not have vaccine mandates and subsequently unvaccinated workers. So they capitulated and put the mandate in place and my friend staged a “sick out” and refused to return to work until the mandate was lifted or resolved in court. He is in a critical position for the company at this point so he kind of had them over a barrel so to speak. After a few weeks, the president of the company privately told him he agreed with his position and asked him personally to submit a request for a waiver. My friend said he did not religiously object but he objected on the grounds that when he served in the military he served to protect and defend the constitution of the United States, not some dictatorial regime. So, in his request for a waiver he very eloquently stated the same and his company granted the waiver.
He stood by his principles and did not lie or deceive anyone in his waiver request, but made his point very clear.
businesses from maintaining their own private mandates (subject to law and contract). >>> The only things that will stop the mandates.
1. CEO’s start dying from adverse effects of the vaccines.
2. EUA is terminated.
3. States enforce Liability for adverse reactions at both company, pharma and govt.