Berkeley asserts that it is meaningless to speak of things-in-themselves that are not subject to human evaluation. Given that, no ampliative judgements can be made by postulating a causal relation between the so-called noumenal and phenomenal realms. It seems that Kant would agree with Berkeley on the former point, but disagree on the latter. If Kant disagrees, then what are his reasons for doing so?
I am not much of a Berkeley scholar so my answer will primarily be an attempt to explain Kant with reference to the things you state in your question.
I think we need to be very careful about what exactly we mean by
it is meaningless to speak of things-in-themselves that are not subject to human evaluation.
This sentence can have several different meanings, which may be creating a false sense of agreement between the positions of Berkeley and Kant. For Kant, the sentence:
We do not know about things in themselves
would be true. But that's no identical to "it is meaningless to speak ..." To understand why, we need to attend to what Kant means by "know" and "understand." For Kant, understanding is something we bring to our interaction with things. Or to state it more clearly. He thinks there are:
And that things when rendered under for the forms of sensibility (space and time) are sensibles for us. And then when subject to the apparatus of the understanding (which for him is 12 categories) become objects of our knowledge. In other words, Kant's claims about not being able to know things is an epistemic claim -- rather than a metaphysical one. In fact, it hinges on a metaphysics of understanding where such things do exist but are restricted from our knowledge precisely because the process of knowing makes them sensibles and then objects for us.
I take it that Berkeley's idealism is suggesting more of an Occam's razor regarding the metaphysical existence of things like things-in-themselves, i.e., if we cannot encounter them in our world of ideas, then we should not speak as if they exist.
A second potential point of confusion is that you're identifying things-in-themselves with noumenon. But this interpretation of Kant is problematic. phenomenon / noumenon is a pair of terms that refers to things-as-we-encounter-them and then on the side, certain types of things we cannot encounter, which seems to include the wills of other rational creatures, our own internal maxim, and other things that are not necessarily things-in-themselves.
Thus, we need to consider the second point where they disagree and how best to word that. Here, I want to focus on
by postulating a causal relation between the so-called noumenal and phenomenal realms.
There's (at least) two problems with this language for Kant and the Kantians. First, Kant does not think we postulate causal relationships; he thinks we impress these on sensibles as part of the act of understanding. Second, there is no causal relationship between noumenon and phenomenon in Kant's view, because causality is something we bring in understanding, and we don't understand noumenon.
In fact, this is part of the point. Morality lies outside of our understanding for Kant. We don't know how people behave morally since we do not have access to the rational will that can act outside causality -- either in ourselves or in others.
This, however, might not assuage your worries since we (or at least I) sure have been talking a great deal about things that I'm claiming Kant says we cannot know/understand. The trick is that Kant's philosophy is not about understanding alone -- but also about reason, which he takes to be our highest faculty. And we can through reason deal with things that we cannot understand, viz., noumenon and the structures that operate in metaphysics.
Will this convince the Berkeleyian or Humean? I doubt it. But for Kant, what we are doing when we talk about things-in-themselves is discussing something that reason proves is necessary to the process of understanding.