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Yes, you can go back to the editors to defend your points--respectfully, of course. Don't be rude. You will need to be clear about what the "wrong impression" is that people might have, and why it would be bad to leave that impression. But you may not be able to get the editors to agree with you. If they dig in their heels, as you say, you have to decide whether to dig in yours. Is the text they cut so vital? If people interpret results too strongly, might it lead them to --for instance-- adopt policies that create great harm to others? If so, then you may decide to withdraw the piece based on principle. Most issues don't rise to this level, and you will simply gracefully accept the editor's judgment. You have to feel really really strongly to withdraw a piece. This may mean that it will be hard for you to publish in that particular outlet in future, so you can't do this lightly. You may be uncomfortable with the cuts to what you view as important detail because you are more used to the demands of scholarly publishing. Remember this is a blog post and not an academic paper. It is geared towards a broader audience, one which may not appreciate nuance and subtlety. This kind of writing demands a bolder style that states results with a lot more confidence than the way we hedge more scholarly writing. A blog post is the start of a conversation, not the end. You should read the comments on your post (well, avoiding bots and trolls), and respond by sharing the nuances left out of the original piece, and --this is key-- linking to your more extensive, detailed, nuanced scholarly article.

Yes, absolutely. Bear in mind that there may be shorter ways to say something but you should ensure that the piece conveys your meaning accurately.

Yes, you absolutely can and should go back to the editors to defend your point. If you believe that the current version misstates your findings, then you should approach the editor and ask for the opportunity to revise (or reinstate) those cut sections. Explain that you understand your first cut at the sections was "too detailed and nuanced," but that the piece is misleading if the author's caution about weak statistical significance is cut. Perhaps there's another way to restate these sections? If, however, the editor does not permit revisions, and if the author believes that the blog post would be misleading as published, then I don't really see another solution other than declining to publish it. The topic is a sensitive one; misleading the public could potentially cause harm. If the editor dug his heels in, I would politely decline to publish in that venue and seek another outlet for the original, more nuanced, blog post. Again, if this were simply a stylistic matter, then the issue won't be so serious. But if the edits misrepresent the strength or nature of the findings, then the author shouldn't publish (and likely wouldn't want it published in that state).