Related to this question.

For polynomial $f$, let $rad(f)$ denote the radical of $f$, the product of irreducible factors.

Suppose that $G(x,y) \in \mathbb{C}[x,y]$ is homogeneous without any repeated factors. $r(u,v),s(u,v) \in \mathbb{C}[u,v]$ are coprime. At least one of them depends on both $u,v$, i.e. is not univariate.

Q1 Is it true that $\deg{(rad(G(r(u,v),s(u,v))))}\ge \max\{\deg(r),\deg(s)\}(\deg(G)-2) + 2$?

If we drop the restriction to depend on both $u,v$ this is false.

The bound is attainable.

Added

Pasten's comment essentially disproved Q1.

Let $r,s \in \mathbb{C}[u_1,\ldots,u_n] $ be coprime.

Q2 Is it true that $\deg{(rad(G(r,s)))}\ge \max\{\deg(r),\deg(s)\}(\deg(G)-2) + 1$?

I suspect $abc$ implies this, so $abc$ for multivariate polynomials might solve this.