He says that shall-issue can continue assuming the requirements are not arbitrary. Essentially, you can have prohibited persons and a licensing scheme can be imposed to weed them out.
However, this section of Kavanaugh's concurrence is interesting:
"Going forward, therefore, the 43 States that employ objective shall-issue licensing regimes for carrying handguns for self-defense may continue to do so. Likewise, the 6 States including New York potentially affected by today’s decision may continue to require licenses for carrying handguns for self-defense so long as those States employ objective licensing requirements like those used by the 43 shall issue States."
So give it, oh, 12 years to find that "suitability" is not objective. Also, a concurrence does not have the same force as the main opinion.