They can continue operating until the courts stop them. Chevron deference is in reference to court cases, not specific regulatory authority. So the Chevron doctrine was that courts should defer to the regulatory agency in most cases. With it gone, courts can generally rule against specific regulations without fear of being over turned on appeal.

The real danger is SCOTUS in another case in the last few days completely removed something called standing in relation to these regulations. It used to be that you could only challenge a new rule or regulation right after it was made. Now you can challenge it when the damage occurs. That sounds better but in reality it’s worse. Because corporations can act as people in court, all you have to do is incorporate a new corporation in a friendly court district. For example, the second you create a “alcohol distribution” corporation you are subject to those regulations. Some of them are a hundred years old. You can now claim damage has occurred and sue to block the enforcement of those regulations.

Before Chevron was removed though the courts would have most likely ruled against you because the agency was deferred to in most cases. Now the court can take this shell company’s case and rule however it wants.