Maybe. Maybe not. Ohio is an at will employment state. If you have a written contract, the employer has to follow it. If you do not, and are not part of a union, then you could face termination.

Start by talking with your employer. See what you might be able to work out with your employer about your situation. Perhaps you could go to a shift with fewer customers during the day? Perhaps you can get a set of shifts on the less attended days of the week, if that applies. Perhaps your employer is looking for ideas on how to separate employees from customers via a temporary physical barrier. (Construction workers are essential workers, too. I bet a team of contractors could build rapidly a frame a see through set of panels to help separate employees and customers.)

Under Ohio's current Stay at Home Order (March 22, 2020), you are an employee of an Essential Business as you said. (Stay at Home Order, p. 5, para. 12.h. (Order), link found here: https://content.govdelivery.com/attachments/OHOOD/2020/03/22/file_attachments/1407840/Stay%20Home%20Order.pdf) That is not the end of the story, though. As an Essential Business, your employer must follow certain steps to minimize your exposure to the Wuhan flu (aka Covid-19 disease).

For example, under the Order, the Employer must comply with social distancing requirements. (Order, p. 8, para. 15.) It must designate six-foot distances. It must do so via signage, tape, etc. to indicate for employees and customers where customers are to stand while waiting for service. (Order, p. 8, para. 15.a.i)

Your employer must provide hand sanitizer and sanitizer products "readily available for employees and customers." (Order, p. 8, para. 15.a.ii)

Your employer must provide separate hours for the elderly and the vulnerable. (Order, p. 8, para. 15.a.iii.)

Your employer must post online what services it is providing at a specific location, how best to reach the facility and to continue services by phone. (Order, p. 8, para. 15.a.iv.)

The caution here is an opt out phrase, "where possible." That is, other than six-foot social distancing, items 15a(i) to (iv) are not mandatory due to that phrase, "where possible."

I would argue that the employer has to provide a safe place for you to work, under the Order at least. If you think your employer can provide the foregoing protections, here's an argument (and not a guarantee). Ohio prohibits terminations of employment that violate public policy. Here, we have an Order that says, essentially, (i) be safe; (ii) minimize social contact; (iii) maximize protective actions (at one point, the Order even directs people how to sneeze (into the elbow or onto a sleeve, not into a hand, (Order, p. 8, para. 15.) I would argue that a person terminated under your circumstances ought to recover damages, at the least recover unemployment benefits.

So, I offer no guarantees ever and no legal advice through a public forum. I think you need to seek the advice of a lawyer who might be able to help you identify options. I hope this helps.

Talk with your employer and see what they say. Most of them are being more flexible now. If there are confirmed cases at work or nearby, that would probably also help your case to your employer.

Attorney James J. Hux
Hux Law Firm, LLC

Yes, you can be fired for not going to work. If your employer is open for business and you do not come to work, you can be fired. There might be some exceptions if you have a specific reason to believe you are at high risk (or, of course, if you are ordered to quarantine, for example), but a general fear of getting the Coronavirus and transmitting it to others does not offer job protection.

Unless you have an employment contract or are covered by a union, or unless the governor issues some emergency order preventing firing, then your employer could fire you. Whether or not you would have a claim for wrongful termination is unknown, since cases like this might never have happened before. Talk to your employer and try to work it out.