Synthesis: The answer to this question,

Does the left have anything to offer to Russia, China, etc? What does it mean for us to support them, or to withdraw our support?

is that it is inconsequential what an individual leftist believes, but it matters a great deal for national leftist organizations to connect and build solidarity with international leftist organizations. What the American left (for example) has to offer China is quite simply a counterpart in America which can participate in the broader socialist movement, which is mutually beneficial. If/when shit does hit the fan, the left has to be ready both theoretically and organizationally.