The relevance here is that if the LA Times loses the the affluent yuppie types retailers target its circulation and profits go down, and increased circulation among Los Angeles's remaining conservatives won't compensate for those financial losses.
The Times still turns a profit now (barely). If the Kochs take it in a conservative direction there's no guarantee that it would better the paper's financial condition, given what LA has become, and they'd have to make good the losses. But who knows? If you have the money, you can take the risk.
The Kochs could influence Times readers in subtle ways, making them more open to libertarian thinking while not challenging their lifestyle choices. That may be what LA progressives fear. If it plays out that way, the results would be a mixed bag for traditional conservatives: more libertarian sentiment in economics, but also less support for traditional social values.