Triviality of actions of compactly supported diffeomorphism groups on the circle

Let $M$ be a connected $C^\infty$ manifold without boundary, let $r\geq 1$, and denote by ${\rm Diff}^r_c(M)_0$ the identity component of the group of compactly supported $C^r$ diffeomorphisms of $M$. Let ${\rm Diff}^0(S^1)$ be the group of homeomorphisms of the circle. Triviality conjecture. Any homomorphism

$${\rm Diff}^r_c(M)_0\longrightarrow {\rm Diff}^0(S^1)$$

is trivial if $\dim(M)\geq 2$. This asks whether the known triviality results for actions on one-manifolds remain valid when the target has only homeomorphism regularity; the supplied text does not indicate whether the statement has been resolved.