It depends on whether you are in a "right to work" state or not. For example, Texas is a right to work state. In Texas, Equity auditions are "open" because they have to be. However, they do not make it convenient for "non-eq" performers to audition.
With AE performers, you get a time for audition scheduled. You MUST be allowed to audition within 15 minutes of your appointment. Auditions only have certain times of the day where they can take place (like 8-5). Non-eqs audition whenever the producers get around to it. Often, auditions will be scheduled to start at, say 2PM, but there will be AE auditions scheduled to take place until 5PM.

Then, the producers will break for dinner, and come back to hear non-eqs...that means non-equity auditions often do not start until 7PM, and some of those people will have been waiting since 2PM. Then, producers will sometimes call people in "in groups", and cut you before you even get the chance to sing, just based on looks. Being non-eq, and auditioning at equity auditions CAN be a total nightmare!!
However, it depends on what type of contract the producer has. If they have a LORT contract, and are only required to hire 1 or 2 equity performers, they will be ACTIVELY looking for non-eqs because they can work them harder and pay them less. If that is the case, your audition process will be much better.
Of course, I don't know if Jersey is a "right to work" state. If it is not...then, you will not even be let NEAR the door to audition. Equity would be all over the producers' butts if you were allowed to audition at an equity call, and you were not a member.