Do maxima in Gibbs energy also correspond to equilibrium positions?
G vs. $\xi$ does not have a maximum

If all reactants and products are pure liquids and solids, G vs. $\xi$ is linear. If some of the species are in mixtures, the entropy of mixing is responsible for the "sagging" shape of the curve. If the curve has an extreme value, it will be a minimum.

Analogy to mechanics

In mechanics, this situation would be called metastability. Giving a nudge in either direction will allow the system to reach lower potential energy.