Does this ruling have any effect on MO and GA?
I don't think directly. Have thosoe two been appealed and stays been requested for the Nov election? This ruling is a stay to put the law back in effect until after the election when the constitutionality of it can be debated further ...
No it is not a ruling on the merits. It is simply another overturning of the nonsense that comes out of the 9th Circuit. In this case the 9th Circuit granted an injunction disallowing the Arizona law to take effect. However, the SCOTUS held that as usual the 9th Circuit had no basis for doing so. So the holding is a procedural one.
It will not affect the Missouri opinion, which was decided on state constitutional grounds. The only affect it could have is to cause the MO Court to reconsider, but that court is the final arbiter of its own Constitution. In this case where its Constitution is interpeted as being more strict than the federal constitution but not violating it, their ruling will stand.
Georgia is another story. The court there is one that was carefully selected by Dems. While not a substantive ruling, it sends a powerful message (a request to Kennedy to lift an injunction referred to the whole Court, which acted unanimously) to lower courts not to mess with elections in such a manner, so close to an election. Though I am not sure procedurally where that case is, this ruling might give the appellate court a reason to allow the photo ID requirement to remain while the case is decided.
It also may affect the 7th Circuit's deliberation in the Indiana case in which oral argument was heard last week. Widely predicted to uphold the photo req., this may give them some confidence to be bold.
It has no effect in GA for the Nov. elections, unfortunately. The dems want all the felons, illegals and dead voting here.