Justice Thomas has been fighting a long battle trying to restore the Privileges or Immunities Clause of the 14th amendment after it was effectively removed from the constitution in the Slaughter-House Cases. He'll often issue dissents or concurrences just to raise the issue of the Privileges or Immunities Clause.
The Institute For Justice (who argued this case, somewhat coincidentally) has a podcast about the 14th Amendment called Bound By Oath. They talk in depth about the Slaughter-House Cases and The Privileges or Immunities Clause in the third episode if anyone is interested in learning more.
Tl;dr It means that the incorporation only applies to CITIZENS, not persons. So citizens united wouldn't apply to the states, but neither would the bill of rights to non-naturalized immigrants with regards to the states.
Thomas would quite happily overturn this line of reasoning just to get the government back to the business of just enforcing contracts. I'm sure he'd be happy to let workers sign themselves into slavery again. Daniel Webster must be applauding from his grave.
The Institute For Justice (who argued this case, somewhat coincidentally) has a podcast about the 14th Amendment called Bound By Oath. They talk in depth about the Slaughter-House Cases and The Privileges or Immunities Clause in the third episode if anyone is interested in learning more.