Except you're ignoring the little fact that the majority of the Abkhaz are Orthodox Christians, so are the Armenians who live there and the Russians who live there. So were the Ossessians who had come to assist them too. Woops.
Hundreds of volunteer paramilitaries from Russia ( including Shamil Basayev, a little known former Russian army officer at that time) joined forces with the Abkhazian separatists to fight the Georgian government forces (see Wall Street Journal: Vladimir Socor, A Test Ground of Putin's International Conduct). In September, the Abkhazians and Russian paramilitaries mounted a major offensive after breaking a cease-fire, which drove the Georgian forces out of large swathes of the republic. Shevardnadze's government accused Russia of giving covert military support to the rebels with the aim of "detaching from Georgia its native territory and the Georgia-Russian frontier land". The year ended with the rebels in control of much of Abkhazia west of Sukhumi. Significant " (The mass expulsion and killing of one ethic or religious group in an area by another ethnic or religious group in that area) ethnic cleansing" occurred on both sides, with Abkhazians displaced from Georgian-held territory and vice-versa; some 3,000 people were reported to have been killed in this first phase of the war.
Remember how Stalin joined forces with Hitler to conquer Poland? Later Hitler attacked Soviet Union, do you see similarities?