A standard traffic ticket and an unpaid fine on their own will not prevent you from being approved for visitation at a California Department of Corrections and Rehabilitation facility. Those are minor infractions that do not show up as disqualifying factors in a background check for visitation purposes.
The only scenario where this becomes a problem is if an unpaid fine led to a missed court date and a bench warrant was issued. That is the question worth sitting with honestly before you go through the visitation approval process or show up at a facility.
Here is why it matters. When you apply for visitation, CDCR runs a background check that includes a warrant search. If a bench warrant exists in California's system, it will surface during that check. At that point the facility may deny visitation, and depending on the facility's protocol, law enforcement could potentially be notified. Showing up at a prison with an active warrant is not a situation you want to find yourself in.
If you are not sure whether a warrant exists, the safest move before applying for visitation is to check your own record. You can do this by contacting the court where the original ticket was issued and asking about the status of the case, or by doing a public records search on your name. An attorney can also run a warrant check quickly and help you address any outstanding issue before it becomes a problem at the prison gate.
If there is no warrant and the ticket is simply unpaid, go ahead and apply. A traffic fine is not a barrier to CDCR visitation approval.