The rationality conjecture for a Du Bois divisor

Let $X$ be a reduced scheme of finite type over a field of characteristic zero, and let $D$ be a Cartier divisor with Du Bois singularities. Assume that $X\setminus D$ has rational singularities.

Rationality conjecture for a Du Bois divisor. Then $X$ has rational singularities, and in particular is Cohen–Macaulay.

This is proposed as a conjectural generalization of the result that a Du Bois Cartier divisor with smooth complement forces the ambient variety to have rational singularities. The source gives no resolution of this stronger statement.