To refer to "inclusive language" as an etiquette is to suggest the adoption of its grammar is a matter of manners.
Such an adoption is fine. As a matter of manners, there are lots of perfectly good words I try not to use in many circumstances. And although grammar is necessary for reliable communication, the particular rules of a grammar are more or less arbitrary, and appeal to one as much as a matter of taste as of reason. (Thus, pace the Kairos Guy, "they" is in fact a third person singular pronoun under a grammar as valid and comprehensible as Fowler's.)
This will not suffice, however, for many "inclusive language" advocates, who want to both impose it on others and shame those who do not use it -- those who are seen, as illustrated again and again in the comments below, as "refusing" or "resisting" it for political reasons, or perhaps sheer cussedness.
For such advocates, there is something morally wrong with using "man" or "he" in an unmarked sense. It "has conditioned us to think of being fully human as being more male than female," to quote jcecil3, and so serves to reinforce the English-speaking world's systemic sexism.
This proposition is a tough sell for a couple of reasons. First, correlation does not imply causation. It is a fact that in English "man" is used to refer to our species in certain biological, anthropological, philosophical, and theological contexts; it is a fact that some people think or have thought of being fully human as being more male than female. How, though, can it be shown the former is a cause of or catalyst for the latter? This doesn't seem to be a hypothesis that could have much in the way of direct objective evidence.
The subjective evidence for it -- the claims of feminists and others that they feel the language conditions the thought -- runs immediately into significant counter-evidence. What can be done about the many people who deny the language conditions the thought? Who insist they are not being sexist when they say, "God became man"?
The only thing that can be done, with more or less delicacy, is to claim the people who insist they aren't sexist are wrong.
The brute force way of doing this is to say, "You may not think you think men are more human than women, but you really do."
The brute force way is not well-received.
A subtler way is this: "It's not so much that you are sexist, but your actions help perpetuate the structures of sexist sin that pervade our society." This brings us back to the still-unsolved problem of direct objective evidence, but it also attacks the deniability of the alleged sexist. I may know I don't think men are more human than women, but how do I know there's no rube who hears me say, "God became man," and thinks, "Aha! So men are more human than women!"?
But what a hypothetical rube might think cannot be very high on my list of unintended effects to ponder before I act. It cannot be, if I am not to be trapped in moral paralysis.