I think the mitigating factors are:
- the perfect fifths involve the inner voices.
D3 is just an octave doubling, if you eliminate it, you still have the same chords
- Parallel harmony while rare is not verboten in all common practice music.
Parallel first inversion triads is pretty well understood, but Tymoczko's system of parallel triads (page 5, paragraph D in the PDF) is where I first read about parallel 6/3 chords used for descending movement, but parallel root postition triads used in ascending movements.
Now I take notice of parallel harmony, and his point about direction and inversion, seems to be true. I do see parallel root position triads in classical style. It's rare, but when I do see it, it doesn't seem to be accidental. It does seem like it happens in connecting or extending passages, in the same places where you might find harmonic sequences. You might also compare its frequency of use and placement to passages in unison/octaves. Like in a string quartet. Most of the texture is typical four-part writing, but then there are highlights of unison/octave playing. Most of the texture is four-part, but there can be high lights of parallel harmony.
Anyway, if the
C3 was held rather than moving to
D3 the chords would be the same and the parallel fifths avoided, so it doesn't seem to make much difference to have the
D3 in an inner voice, that only doubles at the octave, and adds nothing else to the harmony, except perhaps the "trembling" sonority of a major second in a low register.
Parallel root position triads, two examples:
L. Mozart, Nannerl Notebook, No. 34
Dabney, Twelve Minuets and Twelve Dances
The first being a very famous pedagogical source - not where I imagine finding a harmonic faux pas - and the other a run-of-the-mill set of dances. Actually, some other examples of parallel fifth occur in the dances sets I've collected, and they always interrupt my sight reading... because I think I made a reading mistake!