The singularity conjecture for reducible character representations

Let $G$ be a reductive group, let $r$ be the rank of the free group, and write $\mathfrak{X}_r(G)^{\mathrm{red}}$ and $\mathfrak{X}_r(G)^{\mathrm{sing}}$ for the reducible and singular loci of the character variety $\mathfrak{X}_r(G)$. Singularity conjecture. If $r\geqslant 3$, or if $r\geqslant 2$ and $\operatorname{Rank}(G)$ is sufficiently large, then

$$\mathfrak{X}_r(G)^{\mathrm{red}}\subset \mathfrak{X}_r(G)^{\mathrm{sing}}.$$

For $G=\mathsf{SL}_n$ or $\mathsf{GL}_n$, the corresponding equality of smooth, good, and irreducible loci is known when $(r-1)(n-1)\geqslant 2$, whereas the analogous statement fails for some other groups, including $\mathsf{P}\mathsf{SL}_2$. The conjecture asks for reducible points to be singular under the stated rank hypotheses.