The squarefree conjecture on arithmetic progressions

Let $f\in\mathbb{Z}[T]$ be primitive and squarefree, let $\mathcal{A}=a+N\mathbb{Z}\subseteq\mathbb{Z}$ be an arithmetic progression, and let $\mathcal{A}(X)=\{t\in\mathcal{A}:|t|\leq X\}$. Write $Sqf_{\mathcal{A}}(X)$ for the number of $t\in\mathcal{A}(X)$ such that $f(t)$ is squarefree, and let $C_{f,\mathcal{A}}$ be the associated density defined in the source. Squarefree conjecture on arithmetic progressions.

$$Sqf_{\mathcal{A}}(X)=C_{f,\mathcal{A}}X+o(X).$$

This predicts the asymptotic density of squarefree values of a polynomial along any arithmetic progression. The source states that it is known when every irreducible factor of $f$ has degree at most $3$, but gives no resolution in the generality stated here.