The issue concerns the apparent requirement of a mesorah, a tradition, of kashrut for any bird, despite the fact that this is not a Talmudic requirement (see Rema YD 82:3). Since the turkey is a New World bird, there could never have been a mesorah, and yet it is clear that the bird was accepted as kosher. By the 19th century the question was more about how or why it could be, rather than any serious attempt to rule that it isn't kosher. The question often focused on whether or not a community may rely on another community's tradition, and especially whether this is permissible when previously one's own community had not availed themselves of relying on another tradition. That being the case, maybe not eating the bird in question is itself a tradition, not to be discarded. (On this issue generally, see this article by Rabbi Ari Zivotofsky.)
In addition, the sources also reveal a certain confusion as to whether or not everyone is even speaking of the same bird, as well as what the actual place of origin of the bird is. It is no secret that the turkey was widely thought to originate in India, or somewhere else in the East. In this excerpt, addressed to R. David Deutsch, R. Aszod discusses the idea that perhaps we cannot accept a tradition from India, since it lacked great Torah scholars. He rejects this suggestion as worthless, because actually we don't know that they don't have Torah scholars. Absence of evidence is not evidence of absence. He gives the analogy of Eretz Yisrael which at present has 7000 Sephardi men residing there. There is no doubt, he writes, that they have many gedolim, ge'onim in Torah and the two Talmuds and the posekim. We simply have never heard of them, and we never read their writings. Similarly, in India there are many cities and villages with Jews, in the thousands, as we can see in Sefer Shevilei Olam by Rabbi Samson Bloch. We also see this in Maggid Chadashos (the essay on the Cochin Jews) by Rabbi Naftali Herz Wessely Zatza"l, in Hameassef 5550 (1790). Israel is not orphaned in any place they reside. Every large settlement has posekim, gedolim, zaddikim, and scholars, in all times, even if we have not heard of them. If it is permitted in a location, it is because their Bes Din established that their mesorah is valid, with proper procedures, and therefore it was permitted to them.
He then cites an unnamed German rabbi who states that in locations where itis known that there are no Bnei Torah, gedolim or posekim, then you cannot bring proof from their practice.
All of this pertains, by the way, not only to India, but also to England. He had conducted a correspondence with Rabbi Nathan Marcus Adler of London about the kashrut of the English hen, and he was assured that in London they have a mesorah to eat it. He goes on to continue that this unnamed rabbi took London out of the equation, because it is and was a town full of Jewish sinners. He even quotes the Chasam Sofer to that effect, that even 80 years earlier, that was how London was to be characterized. R. Aszod dismisses that point, because at the time London had a great ga'aon for an Av Bet Din, namely Rabbi Tevele Schwar [sic; a printer or transcription error; I am pretty sure he means Tevele Schiff, who was the rebbe of R. Nathan Adler, the Chasam Sofer's own rebbe. On him, see here). This same rabbi exerted great efforts to make sure that things were conducted according to halacha.
We see important things here.
1. He expresses what I believe is the real traditional attitude toward other Jewish communities, that their status as kehila kedosha is real and undisputed (it derives from the presumed presence of scholars and pious people).
2. He quotes Samson Bloch and Wessely (from Hameasseph, no less) and he adds Zatza"l.
Rabbi Yehuda Aszod (1796-1866) wasn't some liberal, nor was he unaware of or disconnected from the struggles over Reform and other kinds of changes in the religion of the day.
Incidentally, the story around his portrait is pretty gruesome and outrageous. For pietistic reasons he refused to pose for a photograph. It is claimed that the following portrait was taken upon his death, when he was dressed, given a Gemara to hold, and his body arranged in the pose. However, it should at least be mentioned that reportedly the proceeds from the sales of this portrait were used to help marry off his daughters.
For more information, see the sources cited in Richard I. Cohen's Jewish Icons: Art and Society in Modern Europe. and this great Seforim Blog post (link).
Getting back to the idea I was discussing, we may find a similar thing in the writings of the Chasam Sofer. An issue arose concerning whether or not a shaliach tzibbur should not wear wool, which developed as a Chasidic custom. The Yismach Moshe defended it, and also claimed that the Sephardim have such a custom, and it is Lurianic. The Chasam Sofer writes (OC 16) that he knows that of the Western Sephardim of Amsterdam, London and Hamburg, this is not true. What do we see from this? Even though the Western Sephardim were clean-shaven, even though they were mostly descended from Conversos, even though they didn't cover their heads all the time, even though they dressed like English or Dutch or German gentlemen, even though their rabbis were called Reverend Dr (at least in London) - they are the Sephardim, and their customs will tell us what the authentic Sephardic custom is, and that's how to establish the facts.
This, by the way, was the Haham of the London Sephardim at the time: