I was trained as a linguist. One thing we do is called "morphemic analysis." Take words and break them up into their bits, link meanings to those bits, and figure out how people form words and how people understand words.
So "thankfully" would be "thank" (noun), "ful" (a nifty way of making a specific kind of adjective out of a noun), and "ly" (making the adjective into an adverb).
One old-fashioned way of doing this--we're talking 1960s or before--had a kind of template or pattern set up, with all the little bits fitting into slots. The problem was a lot of words don't have things in those "slots" where they should have them. It was really, really obvious that they needed to be there.
Take "dog" as an adjective: "dog whistle". It has nothing where it should have a bit of word that says, "Hey, this is an adjective." Since that slot had to be filled, with a perfectly straight face it was proposed that there were "zero morphemes." Little bits of words that had meaning but were perfectly silent and completey ignored. There were lots of them. Everywhere you looked you found them. It was really obvious--they were exactly where you expected them. This bothered people.
Of course, the problem with zero morphemes is figuring out where this completely ignored silent "bit". If there's no trace that they're there apart from your linguistic theory, are they really there or is it your theory that's a bit off? What's the evidence that there's not a zero morpheme in the word "is"? How do you not only show where they are--theory does that--but also where they aren't? How do you falsify the theory? Or is it a matter of faith?
It didn't take long for a better theory to come along, one that removed zero morphemes from linguistics. Yet in the 1990s I was still taught this theory, and I had one professor who still used "zero morphemes," at least for some things. A lot of other things like zero morphemes have come along. Noun-verb incorporation. Trace theory. Residue theory. But they all have the same problem--showing that the silent bit that has to be there really is there and isn't "silent." And if it's not really silent, then you don't need "zero morphemes" or "silent elements."
The thing about dog whistles is that unless you're actually a dog, with canine teeth, a tail, and a baculum (if male, at least), you can't hear them. They're silent. And if they're not silent, then they're not dog whistles, at least not in the sense you used the term.
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