Is it acceptable to extend results from an arXiv paper that has not appeared in a journal? In general, building on unpublished work of another author, which he may have told you in  confidence, or you may encountered as a reviewer or by word of mouth or other informal means, is not an acceptable practice. Does the same apply if the author has uploaded his work on arXiv?

Here's a specific scenario: Suppose I submit a paper for review to a journal. The paper has results that could possibly be extended, however, the idea for extension is either not obvious or is not compatible with the theme of the paper, so I may plan to keep it for a  later paper. If I put the paper on arXiv would it be considered ok if someone else extends my results? This would ruin the theme of the other paper I wanted to write with the extension.

If this happened to me it would make me uncomfortable, as if my confidence has been breached. I don't know if this feeling is justified. This feeling stems from my view of arXiv. My personal theory is that arXiv is an informal medium, unlike journals and conferences, and in that sense it is no different from other channels of informal communication. It allows for structured and faster dissemination of work (thus inform the ongoing work of others), in addition to establishing priority of results, but that does not grant it a formal status. I think an author should exercise restraint in extending results from arXiv, and apply the same standards that he would if he were to encounter the work through classical informal channels.

Of course, this is just my theory. I would like to hear what others have to say about this issue.
I understand your logic, but I do not think that many people treat papers on arXiv in that way.  Papers on arXiv are public unlike the papers you reviewed or the work you just heard by personal communication.  As such, extending the results in a paper on arXiv is a perfectly acceptable practice as long as the second paper cites the paper on arXiv properly.