The 14th Amendment limits state authority by mandating that no state can make or enforce laws that abridge the privileges or immunities of citizens, deprive any person of life, liberty, or property without due process, or deny any person within its jurisdiction the equal protection of the laws. This creates a constitutional floor below which states cannot go in terms of restricting rights.
For example: If a state attempts to impose a voting qualification that effectively discriminates against a protected class, it would likely be invalidated under the equal protection clause.