Is selling non-authentic sports jerseys illegal?

It depends on whether you would be using any trademarks or other intellectual property of someone else.  For example, you couldn't use the particular interlocking "NY" design used on Yankee caps because that is a trademark of the New York Yankees.  The Yankees may have sold the trademark to MLB Properties or some other entity, but the point is that you can't use it for your commercial purposes without the trademark owner's permission, which you would have to pay for.