A query regarding the hierarchy of monotone Complexity Classes
Raz and McKenzie, Separation of the monotone NC hierarchy, showed that the monotone NC hierarchy is strict, and separated it from monotone P. In all of these separations, the upper bound holds for the uniform class while the lower bound holds even for the non-uniform class (so by monotone P, they really mean monotone P/poly).

Monotone P is easy to separate from monotone P/poly since the latter contains uncomputable functions. For example, the language $\{w : |w| \in K\}$ is in monotone P/poly for any $K \subseteq \mathbb N$, but isn't in monotone P if $K$ is uncomputable.

(By the way, there are several reasonable ways to define monotone P, and I'm not sure they are all equivalent. However, all of them should satisfy what I wrote in the preceding paragraph.)