I wasn't actually able to find out which exact dialects of German Plank is talking about. The Wikipedia article on "Bavarian language" lists /p b/ and /t d/ as phonemes alongside /k ɡ/, and says that "Some dialects, such as the Bavarian dialect in South Tyrol, realise /k/ as an affricate [kx] word-initially and before /m, n, l, r/".
To be clear, I understand the quoted material to be saying that some dialects of (Upper High) German have no contrast between /p/ and /b/ or between /t/ and /d/, but do have a contrast between /k/ and /g/, which is however neutralized before /l/ and /r/ (it doesn't say whether in favor of [k] or [g]). It may also be relevant that in many German dialects, the contrast between the two series of plosives is a so-called "lenis-fortis" distinction (sometimes realized in the form of an aspiration or duration contrast) rather than primarily being a true voicing distinction.
Other similar things
I found some possibly relevant information on p. 163-164 of "The Swabian voiceless vowel", by T. D. Griffen (1983):
the combination of ge- with [r, l, m, ŋ, w, s, š, f] in western Swabian results in the tenuis, as in [kriəft] < MHG gerüefet (NHG gerufen) 'called' (Kauffmann 1890: 199). While Kauffmann does note that this process has generalized in his dialect areas to yield such forms as [kras] < MHG gras (NHG Gras) 'grass', it is clear in the presentation that even he considers this to be the result of analogy or some other historical process, because the generalized changes are included under the basic combinatory rule involving the prefix ge-.
Moreover, this Anlautsverhartung is at odds with other developments
in the same word-initial environment. As also noted above, this
very same environment (as it stands after syncope) leads to a weakening
in other western dialects, as we find in [grafd] < MHG kraft (NHG
Kraft) 'power' (Bohnenberger 1928a:27), [grọ̃mẹ] < MHG krumme
(NHG Krume) 'crookedness' (Dreher 1919:15), and (grankhuǫit] <
MHG krankeit (NHG Krankheit) 'sickness' (H. Moser 1937:57). To
these examples from Baden and Württemberg, we can also add [bloî] < MHG plâge (NHG Plage) 'plague' from the more western Baden
(Heimburger 1888:236) and even a regular sound law in the eastern
dialect of Lechrain by which [pl) > [bl] and [kl] > [gl), yielding such
forms as [breisə] < MHG preis (NHG Preis) 'cost' and [glagə) < MHG
klage (NHG Klage) 'complaint' (Haag 1898:33).
I don't know whether the sound changes that Griffen mentions exist in any dialects that furthermore lack a distinction between /t/ and /d/ as well as /p/ and /b/, as in Plank's description. I wasn't able to find a description of the phonology and phonotactics of Bavarian.
Alsatian has a native plosive inventory of [b̥ d̥ ɡ̊ kʰ]
Alsatian, which is a High German dialect, apparently has an sound inventory that contains the plosives [b̥ d̥ ɡ̊ kʰ], as well as the affricates [pf ts tʃ]. This isn't exactly a pure voicing contrast (based on the rest of the phonology, I wonder a little whether [kʰ] might be realized like [k͡x]), but it seems similar to the situation that Plank described.
Wikipedia says that [kʰ] occurs only "at the beginning of a word or morpheme, and then only if followed immediately by a vowel", and transcribes klai 'little' (cognate to Standard German klein) as [ɡ̊laɪ̯].
The Wikipedia article on "Phonation" says that Alsatian /b̥/, /d̥/, /ɡ̊/ "contrast with both modally voiced /b, d, ɡ/ and modally voiceless /p, t, k/ in French borrowings".
