Let me start with answering whether you can publish an idea that appears in a blog, without getting into whether you should do it, or whether it is ethically acceptable.
The status of ideas published in non archival venues such as ArXiv is vague; this is even more so for ideas put in blogs/discussion forums (such as SE).
Different venues take very different approaches to non-archival publications. Some venues do not count them as prior work for the purpose of determining precedence and novelty, others do. In other words, the writer of the blog post may not have any real recourse if you take the idea and publish it. You could always claim that you came up with the idea independently and no one could fault you for it. As anecdotal evidence, the current consensus in some CS communities is that ArXiv publications do not count when assessing novelty (and blogs/forums are ignored).
To an extent, such publications are protected by two things:
- Their impact: some non-archival papers have thousands of citations. It would be ridiculous to try and publish the same ideas because everyone in the community knows where they appear. Some authors don't even bother trying to publish these works and rely on their popularity to "protect" them from being scooped.
- The prestige/community standing of the authors. If some big-shot professor puts up an idea on their blog/on ArXiv, it is less likely that their ideas will be plagiarized since their standing in the community ensures that no one will try to rip them off.
I personally think that these two protections aren't great - especially (2): this is because they offer big-name researchers (and their students/group members) an unfair advantage in terms of getting their results out first.
Now getting back to whether you should do something like this. The answer is a clear-cut no. First of all, you probably won't publish first: if someone puts a good idea on a blog, chances are they had already started working on it themselves and are just previewing parts to the public. In any case, taking an idea from a blog without referencing the original is plagiarism: it's unethical, permanently damages your permutation, and is just not nice.
Nothing is stopping you, however, from either reaching out to the authors, or elaborating upon this idea yourself and publishing the additional results (again, with reference to the original). This is definitely allowed.