Lankavatara Sutra Chapter 3, Section LXXV

I'm using the usual translation....and as usual, I'm not authorized to say a word by a teacher;  my words and comments  are mine.

One thing strikes me in reading this;  the Buddhist doctrines of non-duality are clearly in no way  nihilism - that too is a form of discrimination, and falls far short of the fact that t myriad ways in which non-duality presents itself and can be expressed  is asserted  by the Buddha.

To the text...the Fully Enlightened One is neither made nor unmade, neither an effect nor a cause, because if any of these were the cases, the error of dualism would here be committed. 

That which is neither an effect nor a cause, Mahamati, is neither a being nor a non-being; and that which is neither a being nor a non-being is outside the four propositions. The four propositions, Mahamati, belong to worldly usage. That which is outside the four propositions is no more than a word, like a barren woman's child. Mahamati, a barren woman's child is a mere word and is beyond the four propositions [oneness and otherness, bothness and not-bothness, being and non-being, eternity and non-eternity]. As it is beyond them, the wise know it to be not subject to measurement. So is the meaning of all the terms concerning the Tathagata to be understood by the wise.

This text here is folding back on itself; in a sense, but I think in the "standard" or straightforward sense it is simply saying the Tathagata is not comparable via terms like being,  non-being, or effect and cause or neither.

It is folding back on itself because "beyond" is a  term of comparison.

The next points that are made concern the idea of "self-nature" and the relationship of the Tathagata to the five aggregates.  As these points are often discussed in highly abbreviated form (and in my reading some folks pronouncements of the notions of self/non-self in Buddhism diverge from my reading of the intent here) I will quote this in full:

It is told by me that all things are egoless; by this is meant, Mahamati, that they are devoid of selfhood; hence this egolessness. What I mean is that all things have each its own individuality which does not belong to another, as in the case of a cow and a horse. For example, Mahamati, the being of a cow is not of horse-nature, nor is the being of a horse of cow-nature. This [exemplifies] the case of neither being nor non-being. Each of them is not without its own individuality, each is such as it is by its own nature. In the same way, Mahamati, things are not each without its own individuality, they are such as they are, and thus the ignorant and simple-minded fail to understand the signification of egolessness by reason of their discrimination; indeed, they are not free from discrimination. The same is to be known exactly about all things being empty, unborn, and without self-nature.
In the same way the Tathagata and the Skandhas are neither not-different nor different. If he is not different from the Skandhas, he is impermanent as  the Skandhas are something made. If they are different, they are two separate entities; the case is like a cow's horns. As they look alike, they are not different; as the one is short and the other long, they are different. [This can be said] of all things. Mahamati, the right horn of a cow is thus different from her left horn; so is the left from the right; the one is longer or shorter than the other. The same can be said of varieties of colours. Thus the Tathagata and the Skandhas are neither different nor not-different the one from the other.

So the idea of anatman does not exclude the obvious differences found in various existences, and although no doubt cynics might say that the logical constructions here are done to provide the only consistent way out of a paradox where you don't have either a  spirit world apart from the everyday world or a completely "known" universe (I won't use the term "naturalistic," as I think that the idea that "all that is worth existing is what we  can observe" doesn't stand up to history; that is, there's been myriads of stuff we didn't know existed because we didn't observe it, and there are  rationally admissible ways of talking about the non-observable.)

But I don't like the cynical view that this is merely an escape clause out of a messy paradox; rather, to me it apprehends the way we experience the world.  Or at least the way I experience the world.  Perhaps your mileage varies.