Therefore, users should see a warning when they use both symbols in the same post (outside of the context of MathJax
There are, I think, three different use-cases for φ and ϕ:
They're used as letters in Greek words. No-one's going to want to use both variants of the same letter, so it doesn't matter much which one readers see.
They're used as place-holders for numbers, functions, &c. in mathematical expressions. For serious confusion to arise, the writer must first decide to use the two variants to refer to two different things—already rather unfriendly to readers—and second to specify them with MathJax in one place and with Unicode in another—which is hardly good typographical practice.† So for sites with MathJax enabled (which are the ones with more call for mathematical expressions), the solution is to use it consistently, and to encourage others to use it. For sites without MathJax enabled, the worst that can happen is that the variants are transposed for some readers, which again doesn't matter much.
The glyphs themselves are the topic of discussion. Here, without recourse to MathJax, the writer has to resort to images to ensure that all readers see the right glyphs.‡ That's certainly a nuisance; but in mitigation, there can't be all that many actual or potential posts on this subject.
The warning you suggest is a good idea, without a doubt (+1); but I hope it's quick & easy to implement, as the problem doesn't seem to merit many hours of developer time.
† For reference,
\varphi gives the loopy variant and
\phi the stroked variant, both italicized:
This is the default font, MathJax TeX. If it's not installed on a user's machine, MathJaX supplies it (or for older browsers that don't support web fonts, even creates an SVG image file for display).
‡ Perhaps using an on-line utility such as Unicode Image Maker from Browserling:
And, thinking about it a little more, if your post's about the appearance of a character, it's not really a disproportionate burden to have to upload an image of it, and probably considered good practice in general.