In some states you may have protections from a conviction that old being used against you, but you didn't identify the state. The EEOC would be skeptical of the use of such a conviction to deny employment if you're part of a protected group, but we don't have facts on that issue, either.

If there is no legal reason why the employer cannot consider the conviction, then it can be a factor in their hiring decision. I would be surprise if a single, thirty-year-old misdemeanor shoplifting offense was treated as a significant issue, but even if a minor consideration it can make a difference when an employer is choosing between possible job candidates.