Non-density conjecture for product polynomial maps

Let $f(z,w)=(p(z),q(w))$ be the product of two polynomial maps of degree $d$ in $\mathbb{C}$. The non-density conjecture. If $p$ or $q$ belongs to the bifurcation locus in $\mathcal{P}_d(\mathbb{C})$, then $f$ belongs to the closure of the interior of the bifurcation locus in $\mathcal{H}_d(\mathbb{P}^2)$. This conjecture concerns the density of stability and bifurcation for holomorphic maps of $\mathbb{P}^2$, asserting that product maps inherit abundant bifurcations whenever one factor is bifurcating; the question is presented as an open problem.