Schröer's klt type and strong F-regularity conjecture

Let $R=\left(\mathbb{C}[X_1, \dots, X_n]/(f_1, \dots, f_r)\right)_{(X_1, \dots, X_n)}$, where each $f_i\in\mathbb{Z}[X_1,\dots,X_n]$, and let $R\bmod p$ denote its reduction modulo the prime $p$. Schröer's conjecture. $\operatorname{Spec} R$ is of klt type if and only if $R\bmod p$ is strongly $F$-regular for all but finitely many $p$. The only-if direction is known, and the if direction is known when $R$ is $\mathbb{Q}$-Gorenstein or its anti-canonical ring is Noetherian; the general case remains open even in dimension three.