Take that argument one step further. Is Tibet now an integral part of China? Is Taiwan independent of China because it has not been an integral part of the mainland for many years?
In truth, both Ossetia and Abkhazia were intentionally put into Georgia by Stalin to divide and control them. The Ossetians have a claim for reunification, just as Germany did.
Abkhazia is far more complicated, as it was both a part of Georgia and an autonomous republic under Stalin. One of Stalin’s secret police chiefs, Beria, encouraged Georgians to move there. Later, the Armenians and their church encouraged Armenia emigration there.
So the largest minority is not Georgian, but Armenian.
The devil is in the details of autonomy, however. Since 1991, both areas have split off from Georgia. But all this does is make “de jure” what had been “de facto” for many years. The Georgians didn’t rule them before, and they don’t want the Georgians to rule them now.
I will also add that there are enclaves like this all over the region, with lots of the same and similar problems. Chunks of other countries that are occupied by large number of people from adjacent countries.
But unlike the situation in California, where there are just “a lot of Mexicans”, the divisions are far deeper. Had California been an independent place not under US federal law for many decades, or even worse, under Mexican law, even if not policed by the government of Mexico, we would find ourselves in a similar situation.
That is, if the US government hadn’t ruled California since WWII, the vast majority of the people who lived there were Mexicans, and they used Mexican law and spoke Spanish, what right would the US government to now say they want to rule California?
As for the Mexican populated counties along the US-Mexico border, it would be like lifting a burder to US taxpayers if they somehow demanded and were awarded their independence or integration with Mexico. I would willingly give money to their cause provided, of course, we put a long moat filled with crocs along their north border.