The acid bacteria make acid, they don't consume it. Lactic acid, and occasionally acetic acid, are byproducts of the bacteria in sourdough metabolizing sugars. Active yogurt contains its own lactobacillus bacteria, but these will be different strains that thrive in different environments.
According to the interwebs and Google Scholar, the bacteria in yogurt are typically strains of lactobacillus bulgaricus and streptococcus thermophilus.
In sourdough it's typically strains of lactobacillus pontis, lactobacillus sanfranciscensis, lactobacillus paralimentarius, lactobacillus fructivorans, and lactobacillus fermentum. Part of the environment that these strains are especially adapted for is the yeast itself, which is likely to include saccharomyces exiguus, candida milleri, or candida holmii.
The coexistence these bacteria and yeasts works in sourdough because the organisms are mutually tolerant of each others' waste products. Both types of organisms use their waste products as chemical weapons, to discourage the growth of competitors. The lactobacilli produce lactic acid, which inhibits most other bacteria and yeasts (including commercial baker's yeast—saccharomyces cerevisiae). But not our friendly sourdough yeasts. Likewise, yeasts produce alcohol. This discourages most bacteria, but not the right strains of lactobacilli.
This is true up to a point. Eventually the dough can get too acidic for the yeast. This is why it can be hard to get extremely sour bread to rise much.
But the broader point is that bacteria and yeast that thrive in an unrelated environment are not going to thrive on wheat flour. Maybe there's some utility in pre-acidifying the flour, to prevent infection by other types of organisms before these acid-resistant ones take over. That's just a wild guess. But you're not actually going to be colonizing flour with bacteria from fruit or dairy products.
