Non-isomorphism conjecture for proper minor- and union-closed families

Let $\mathcal{F}$ be a minor- and union-closed family of graphs, and let $\cong_{\mathcal{F}}$ denote homomorphism indistinguishability over $\mathcal{F}$. Non-isomorphism conjecture. If $\mathcal{F}$ does not contain all graphs, then $\cong_{\mathcal{F}}$ is not the isomorphism relation. This is presented as a relaxation of the main distinctness conjecture. The paper notes that union-closure is unnecessary for a proper minor-closed class after closing under disjoint unions, and leaves the assertion open.