It is known that odds ratios enjoy a certain symmetry. For example, the odds ratio of outcome $Y$ is the inverse of the odds ratio of outcome $\neg Y$. Risk ratios, on the other hand, do not enjoy this symmetry. However, risk ratios have the property of collapsibility. So adjusting for a covariate that is not a confounder does not change the magnitude of the risk ratio. Consider the more formal definition of collapsibility:
Definition. Let $g[P(x,y)]$ be any functional that measures the association between $Y$ and $X$ in the joint distribution $P(x,y)$. Then $g$ is collapsibile on a variable $Z$ if $$E_{z}g[P(x,y|z)] = g[P(x,y)]$$
So in the case of the risk ratio, $g[P(x,y)]$ would be the risk ratio? What if we don't know $P(x,y)$? A risk ratio is the ratio of two incidence densities which doesn't seem to depend on any probability distribution.