The former Abkhazian SSR, until its subordination by Stalin in 1931, had a constitution of its own. This specified an alliance with the former Georgian SSR, which subsequently specified an equal status within the Transcaucasian SFSR. But because of Abkhazian leader Nestor Lakoba's defiance of central rule, Moscow punished the Abkhaz by subverting them to the Georgian SSR.
If the 1939 partition of Poland and the acquisition of the Baltic nations was illegal, then so was the stripping of Abkhazia's status as a constituent republic with the de-jure right to secede from the USSR.
The Abkhazian fighters were backed by their fellow Circassians and other North Caucasians. Any Russian military involvement was unofficial and no orders were issued from Moscow.
Also, don't forget that other Russian circles backed Shevardnadze.