The Hebrew alphabet has 22 written characters (plus 5 specialized characters for the ends of words - ם, ן, ץ ,ף, ך) generally assumed to be each originally associated with distinct sounds. The Masoretes have a tradition (which to our [traditional] ability, we also attempt to follow) regarding a dual pronunciation of six letters in the Alephbet, namely, ב, ג, ד, כ, פ, ת (typically indicated visually by the presence/absence of a dot in the middle of the character) However, the Masoretes were predominantly from a Karaite-heretical sect. Is there any independent basis in traditional halacha, especially in Chazal, for distinct, contextual pronunciations of these letters? What is the view of linguistic scholars regarding the origin and development of Beged Kefet (and how might this be relevant to halacha)?
Rav Saadiah Gaon writes in Chapter 2 of his commentary to Sefer Yetzirah lays down the correct pronunciation of the Hebrew letters, saying that not only is there בגד־כפת letters, but that even the ר has an alternate pronunciation with a dagesh so more like בגד־כפרת according to him.
He basically says that Hebrew and Arabic share all the exact same sounds, except that Hebrew has a בּ ) ב without a dagesh) that Arabic lacks, פ ) פּ with a dagesh) that Arabic lacks, and Arabic has a Jimmal (the normal English J sound) that Hebrew lacks.
i don't think anyone is about to call Saadia Gaon a Karaite, so you have a clear Rabbinic Posek speaking of the importance of pronunciation.
As for how it may be relevent in Halacha, the Gemara says that one should extend the Daleth from the word Echad until one runs out of breath. This is not possible if you are unable to distinguish between ד and דּ.
"All who prolong the word echad will have their days and years prolonged. Rabbi Acha bar Yaakov said that one should prolong the letter daleth. Rabbi Assi added: Provided that he does not slur over the letter cheth." (Berachot 13b)
Therefore you have at least one instance of the ד having at least 2 distinct sounds by the time of the Talmud.
And while this may not have a direct halakhic significance, it does draw the attention to the proper pronunciation of ו. In modern Hebrew, both ו and ב share the same sound. But according to Saadia, if Arabic doesn't have a ב, then he should have also said ו to go along with it. And he also does not say that Hebrew doesn't have a w sound, that Arabic clearly has. So according to many scholars who read the words of Saadia Gaon, the ו should make the sound of a w.
As a bit of a side note, i haven't personally run across any Karaites that distinguished between all the בגד־כפת letters. So i think the idea of attributing the distingishment of these letters as something linked distinctly to Karaism might be a bit misguided.
There are two points I'll make. But I do hope someone else has a sourced answer.
First of all, this is something 'in the Torah' that these heretics are careful about. Therefore, they have believability as per the first chapter in Chulin regarding the Cuthim.
Second, the Tshuvas HaRashba Hamyuchas LiHaRamban siman 232 which is brought in the Meiri's Kiryas Seffer maamar 2 chelek 3 deals with the issue of finding words written differently in chazzal than they were being written based on ׳חכמי הלשון והספרים המדויקין׳. The halacha was that if the word form in chazzal was the basis of a practical halachic drasha, we go with chazzal's version. If it was brought for midrashic purposes, we go with the mesora version. And if the mesora versions conflict, we go with the majority, as was done in the days of Ezra mentioned in maseches Sofrim 6 4 concerning the discrepancy of three words.
All in all we seem to not mind relying on them, especially where it doesn't really go against any halacha.