 Bernoulli coordinate observable is not almost periodic

For independent fair signs on a two-sided Bernoulli shift, the coordinate observable $f(y)=y_0$ has unit norm and pairwise orthogonal orbit values. Their pairwise squared distance is two, excluding a finite small net in global $L^2$. Its pullback along a factor map can nevertheless be a relatively almost periodic observable, since it is fiber-constant and takes only two values.