How do organisms survive and function despite metabolic activities that tend to shift ph toward either acidic or basic ends of the scale?

The organisms have buffers

The body will produce mixtures of chemicals that resist pH changes,a buffer, which consists of  a weak acid and its conjugate base, or vice versa.
If the pH is too low (acid)  because of the metabolites produced, the base of the buffer will accept some of the hydrogen ions and raise the pH to normal levels.