Q:

Is initial d becoming unvoiced in (many varieties of) English?

I believe I heard once that initial d in English is historically becoming less voiced.  But I cannot find references confirming that.  Is it true?  And if it is, then is it part of an identifiable larger trend?
As context, I believe I heard it from competent linguists talking about the interminable question of spelling Tao versus Dao for the Chinese philosophical term.  The Mandarin word has a  tenuis voiceless alveolar plosive initial.  So the English representation is a big problem.  And I believe one linguist said a complicating factor is that the initial D in English is losing its voicing (which brings Dao closer to the Mandarin pronunciation).  To be clear: I am not asking about the Chinese word.  This is just to supply context for my question.

A:

Word-initial /d/ in English is usually phonetically "devoiced" (a less ambiguous term is "short voicing lag"; sometimes the term "partially (de)voiced" is used but I don't think this is really an accurate phonetic description for plosive consonants). This is something it shares in common with the other "voiced" English plosive phonemes /b g/, and there are also a number of other Germanic languages that show basically the same phenomenon.
But as far as I know, there is no good evidence about this being a "trend" in English; the phenemenon was observed already in 1964 and I haven't read any descriptions that mention it becoming more or less common, or more or less extreme, since then. I would guess it differs somewhat among regional accents, but I'm not aware of any general geographical trends either.
Voice onset time" is a more accurate model than the "voiced/unvoiced" binary
The binary classification of sounds as "voiced" or "unvoiced" is, like many phonetic categories, a simplification of a more complicated situation.
A more accurate model is "voice onset time" (VOT): the time between a stop's release and the start of phonetic voicing.

If VOT is negative (voicing starts a significant time before the stop), the stop is classified as voiced.

If VOT is notably positive (voicing starts a signficant time after the stop) the stop is classified as voiceless aspirated. This is like the "t" in the English word toe. (The typical amount of aspiration in aspirated stops differs between languages; in some languages, there are stop phonemes that are even more strongly aspirated on average than English aspirated stops).

If voice onset time is zero (more or less), than we have what is called a "tenuis" voiceless stop. The usual example given in English of tenuis stops is a stop after word-intial /s/, as in /t/ in stone, /p/ in spot, /k/ in skin.

I mentioned that positive VOT is gradient, so some languages have "stronger" aspiration than others. The same is true for negative VOT: some languages have more "strongly voiced" stops than others (in some languages, there are added complications, like the use of "pre-nasalized" voiced stops, transcribed as [ᵐb ⁿd ᵑg], which start with air passing through the nose).
In fact, different languages tend to carve up VOT into different "categories", kind of like how different languages divide the vowel space into different categories. Like the vowel space, VOT categories are not arbitrary; there are general patterns that languages tend to follow.
A relevant recent Linguistics SE question: Contrast of degree of aspiration in Korean
English voiced stop phonemes may have zero, or close to zero, VOT word-initially
Here is a paper comparing Polish, which has strongly "voiced" word-initial voiced stop phonemes, with English:

VOT in Polish and English - A Pedagogical Perspective, by Wiktor Gonet

Gonet uses the term "partially (de)voiced" and says that

Typical "textbook" English voiced word initial plosives require VOT ranging around 0 (from short negative through 0 to short positive) (82)

I found  a paper that presents some more phonetic detail: Patterns of acquisition of native voice onset time in English-learning children (Joanna H. Lowenstein and Susan Nittrouer). Lowenstein and Nittrouer say that for the children studied

Children’s mean voiced VOTs started at 11 ms [i.e. after release, so phonetically "unvoiced"!], and stabilized at 16 ms at 21–22 months.

They also provide some helpful terminology from the original VOT acoustic study Lisker and Abramson (1964). Lowenstein and Nittrouer summarize the classifications Lisker and Abramson found as follows:

long voicing lead, where phonation starts well before the oral release; short voicing lag, where phonation begins just after the oral release; and long voicing lag, where phonation begins well after the oral release.

These terms may be useful to avoid confusion between "voiced" as a phonetic and phonological category.
Anyway, it's clear that in English, phonemically "voiced" stops in word-initial position are often produced with around 0 VOT ("short voicing lag"), and English speakers tend to perceive 0-VOT stops in this position as voiced stop phonemes.
It's unclear when this occured, but there are parallels in other Germanic languages
English voiced stops might have been more fully voiced/"long voicing lead" in the past, but as far as I know, we don't have great evidence for this (or for any kind of timeline). The Lisker and Abramson study from 1964, which Lowenstein and Nittrouer indicate was the earliest example of measuring VOT, already records examples of English speakers who use short voicing lag for word-initial /b d g/. In fact, three of the four English speakers they studied used this pattern (though the fourth did use leading voicing).
Historically, English word-initial voiced stops in native words come from the Proto-Indo-European (PIE) series of stops written *bʰ, *dʰ, *gʰ, which are most commonly reconstructed as "voiced aspirated" stops (hence the spelling) but there is some controversy about that. In Proto-Germanic, the reflex of word-initial PIE *gʰ is thought to have been pronounced as a voiced velar fricative [ɣ], which did contrast with the reflex of *k, thought to have been a voiceless velar fricative /x/, but we really don't know enough to give a detailed description, and so it seems to me quite possible that Proto-Germanic [ɣ] was partially voiced [ɣ̊] or something at this stage, and later became a short-voicing-lag plosive [g̊] in English without ever passing through a long-voicing-lead plosive stage.
The VOT categories of modern standard German are somewhat similar to those of English, with aspirated voiceless stops and "voiced" stop phonemes that may have zero VOT. Interestingly, due to the High German Consonant Shift, modern standard German /t/ (realized as [tʰ] at the start of a word-initial stressed syllable) corresponds to English /d/, so there was evidently a more drastic, phonemic devoicing of this particular consonant in German's history.
In some Germanic languages, such as Icelandic, it is even common to transcribe the phonemes as voiceless aspirated /pʰ tʰ kʰ/ vs. voiceless unaspirated /p t k/. In others, like Danish, the voiced letters /b d g/ are used (often with the devoicing ring diacritic: /b̥ d̥ g̊/) to represent pretty much the same sound.
Sometimes devoiced unaspirated plosives in Germanic languages are described as "lenis", a fairly vague term that contrasts with "fortis". I think these terms are mainly used to connect various Germanic consonant systems under a kind of umbrella (for example, apparently some dialects of German have a two-way phonemic contrast that isn't realized as a VOT contrast, but as a contrast in some other consonant feature(s) like duration).
The supposed phonetic definition of "lenis-fortis" is based on the idea of "articulatory strength" but I don't know how measurable that is; my impression is, not very.

