I generally do whatever H&FJ did in Whitney (my go-to example for most stuff). I figure that if their customers are happy with it than most people will be.

I understand why some people leave math operators upright, especially in display faces, because nobody is ever going to use them anyway. I do slant them, but I also leave out the extra stuff from Mac OS Roman because nobody uses it anyway.

I understand why some people leave math operators upright, especially in display faces, because nobody is ever going to use them anyway

I thought the point is more that when you actually typeset mathematical formulas you don't want slanted operators, you need upright ones (even though variables etc. may be italicized). Which would imply that upright ones might also be useful in a text face.
However things like the "+" can't only be used for actual math stuff but also as a typographic device, in which case you probably want it to match the angle of the italic. So basically it comes down to what you expect people to use your math operators for. And if you want to be extra generous you just give them both slanted and upright ones.

Many mathematical symbols are such that when a vertical stroke is replaced with a slanted one, it starts to look like it could be a different symbol. The information of "this is definitely supposed to be a vertical line" or "this is definitely supposed to be a diagonal line" needs to be preserved for clarity. Also, variables are usually italic letters, and it takes some of the hassle out of setting equations when you don't have to worry about an ugly sloped plus sneaking in.

When I think there might be some value in the italic being distinct from the roman, I skew the ends of the horizontal strokes.

Thank you all for the advice and insight. I've decided to un-italicize my mathematical operators.

Nina, I might take up your comment about including both (one for mathematical formulas and one for display).

What are everyone's thoughts of italicized diacritics? At the moment, I've decided to leave the acute and the grave at the same slant they are in the Roman for the sake of clarity.

Way back, there were no figures in italic fonts.
A really old-school revival would do likewise.

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There is some cultural history and tradition here.
Folllowing that, it would seem to be more appropriate to have non-slanted non-alphabetic glyphs in old-style faces.

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Nonetheless, I made all the italic math operators in my 19th century revival, the Modern Suite fonts, slanted.
The reason being, that even with its copious language coverage, they are still not math fonts.

IMO, unless one is producing a fully loaded math font, all italic glyphs should be slanted, except ® and ©.

(I did provide vertical parentheses in the Mod Suite italics, as a Stylistic Set.)

I presume the reason for excluding ® and © is to meet legal requirements.

A "really old-school revival", indeed, might note that only very basic punctuation characters belonged to individual fonts, and most other special symbols were sorts. Thus, & and $ might be italicized, but @, #, and % would not be. The obvious reason for not doing it that way is that so doing would be foregoing an advantage the new technology gives us for no good reason.

Even when one isn't doing a typeface specifically intended for mathematics, though, italicizing |, +, =, ~, <, and > does present potential ambiguities. While I would tend to agree this is not an issue with display typefaces, almost any text typeface, these days, could be used, if not for mathematics, at least for programming examples. (But here, italics aren't an issue, unless the original Pascal display format is being used...)

However, it's always possible for those preparing a text to only italicize the variable names, so this is not a critical issue.

Wait, is there a reason for not italicizing ® and ©? I mean if one wants to?

Go right ahead!
Perhaps I shouldn't be so strict, after all I have italicized © and ® in Fontesque (1994-2010) and Alphaville (2000), but nothing else.

Ah, good – thanks Nick.