I have a pretty strong "if the sf aspects aren't important to the story, don't include them" gut feeling. As it's a gut feeling, I don't know that I can rationally justify it or that it'll stand up to close scrutiny, but I'll give it a try. But really, it's a gut feeling, so even if you poke holes in my attempts at justification, it'll still be there.
My favorite example is the story we got a while back in which some space outlaws enter a space Old West town on their space horses, rob the space bank with their space guns, then free their space friend from the space jail. It was a hackneyed and stereotypical Western story, in which the author had changed words like "six-shooter" to words like "ray gun." It obeyed (nay, slavishly bowed down to and worshipped) Western genre conventions; it used the language of a Western except where the author had thought to do a search-and-replace; it had a Western setting and culture and economy and technology (with a light veneer of pulp sf); there was, in short, nothing sfnal about it except for certain pieces of vocabulary and technology that were just thin disguises for something else. In response to my rejection letter, iIrc, the author somewhat sheepishly admitted that he had in fact done just the sort of weak substitution I'd objected to. And why had the author attempted this? As far as I could tell, it was because he had a Western story and we were not a Western magazine, so he put a light top coat on the story to try to fool us into thinking it belonged in our genre rather than his.
Obviously this is an extreme example, and a lot of the problem was that it was a bad Western. I think there's a lot of truth in what some of you have been saying here about other sources of reader pleasure making such things less important -- if it had been a really good story, I would have been more inclined to say "Cool, this is a pastiche about the dangers of genre conventions" or something, or even just to enjoy it on its own terms. I imagine many of you could have written a story that would've more or less matched my above description but that we would've bought.
And yet, for me there's more to it than the sources-of-reader-pleasure. Some people -- myself included, but I think not Ben and probably not most of y'all who comment here -- have a gut feeling about sf. Stories that feel like sf to me feel different to me, at a fundamental level, from stories that feel like, well, non-sf. (Though yes, there are plenty of gray areas.) There's a scene in one of the Edward Eager books when the kids read a book that sounds from the title like it's going to be fantasy but they discover that it's not and they're terribly disappointed; that's me. In that Eager book, iIrc, part of the kids' disappointment was that the story was dull and moralistic and annoying, but I get that disappointment even if the story's a good one. I even got some of it with Andy Duncan's brilliant "The Chief Designer" (and yes, I know the arguments for why it counts as sf (I'm even willing to more or less agree to them), and yes, I voted for it for the Hugo). And I've felt a little uncomfotable when we've published a couple of stories that I've thought were really good but that could only be considered sf by stretching and by calling on the mighty "speculative sensibilities" concept.
Back in 2002, we rejected two good stories by authors we really like because the only sfnal elements in them seemed gratuitous to us. I'm not sure we would make the same decisions about those stories now -- we're a little more willing to stretch our ideas of genre boundaries now, and I especially regretted one of those decisions when the story showed up later in Polyphony and I re-read it and really liked it -- but still: no matter how good the story is, if the only sfnal thing in it is that halfway through the story, an alien lands, waves hello to everyone, and then flies away again (and nobody ever mentions this again), then that doesn't trigger my "this feels like sf" reaction. And likewise if the only sfnal thing is that in the world of the story, horses are called "zorses." This ties in with y'all's previous discussion about taking the story seriously and avoiding having what Ben called "an irritatingly thin world" -- the kind of story that I'm objecting to (and that I think most people who say they want the sf to be integral are objecting to) usually doesn't feel like the world of the story is internally consistent. But for me, that's again a rationalization; my gut feeling says "this isn't really sf," not "this is bad worldbuilding."
There are at least four subcategories of stories that trigger my "the sf elements aren't integral to the story" reaction:
1. Story that in all ways appears to be from some other genre, except that some of the vocabulary has been changed to sf vocabulary without any other changes.
2. Story that has a clearly sfnal (or at least surreal) scene in it that doesn't appear to have any impact on the rest of the story. (I suspect in most such cases the author meant that scene to enrich or refocus the reader's understanding of the whole rest of the story; I like that when it's done in a way that works for me, but I'm talking about the stories where I can't see what relevance the one sfnal scene has to the story.)
3. Story that has only one element that's intended to be sf, but the author doesn't realize it's true in the real world, or that it's only a very slight extrapolation of something that's true in the real world. (Like a story presented as sf in which there's an intersexed character, because the author doesn't know that such people really exist; or the Asimov's story from a few years back in which a repressive government had the amazing high-tech ability to easily edit photographs.)
4. Otherwise good story in which the sf element distracts (for me) from the core story that the author is really trying to tell. There are a lot of writers (myself included) who don't know how to go about trying to sell a non-sf story, and who will thus try to write a given story as sf even if it's not comfortable there. More than once, I've suggested in a rejection that the author consider removing the extraneous sf elts because that'll make it a better story, and then trying to sell the story to literary venues.
I do think there are a lot of gray areas. For example, one of sf's traditional modes is to exaggerate or distort a particular real-world thing, to make a point about it in the real world. That can result in stories where the sf looks like a thin veneer -- like, a story in which there's a superweapon that's just like an H-bomb only a hundred times more powerful! -- but where the sf part is there to make a point. I tend not to like such stories, but they're a very long-established tradition in sf.
And I know that plenty of people just plain don't care about the "integral to the story" criterion. When Mary Anne and I were working on a collaboration a while back, at one point I said something like "Well, I'd like to change this aspect, because otherwise it feels like we're taking exactly the real-world historical situation and setting it in space," and Mary Anne basically said "So what? What's wrong with that?"
But for me, it really does make a difference. I want sf to feel fundamentally different. I want that sense of unheimlich and/or sense of wonder; that feeling of unordinariness; that touch of strange. And if I feel like the touch of strange doesn't add anything to the story, then I feel cheated -- I feel like the story is claiming to be magical, sets me up to expect my unheimlich sensors will be fondled, and then fails to fondle them.