I would like to know if the idea of kavod ha'brios applies to non-Jews as well.
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Per my comment, I'm having a hard time imagining a practical case where it would matter, but I found that Rav Aharon Lichtenstein in an article on the topic thinks that this statement in the Rambam (סנהדרין פרק כד הלכה יז) would indicate that it does apply to non-Jews:
ואל יהי כבוד הברייות קל בעיניו, שהרי הוא דוחה לא תעשה של דבריהם, וכל שכן כבוד בני אברהם יצחק ויעקוב המחזיקים בדת האמת
And [a judge] should not let kavod ha'brios be light in his eyes, since a negative Rabbinic commandment is pushed away for it, all the more so the honor of the children of Avraham, Itzchok and Yaakov who hold on to the true religion.
I guess it depends on where you put the emphasis, on the "children of" or on the "hold on to." In context, where it is talking about decrees made to prevent the breach of Judaism, the former seems the more reasonable one.
If you at the places in ש"ס where the term כבוד הבריות is used, you'll notice that it refers to cases where a Rabbinic prohibition is temporarily abrogated in deference to human dignity. See the top of Shabbat 81b (and pay attention to Rashi) for an example.
See also the Rambam in כלאים י:כט here :
For [the obligation to] honor people at large does not supercede a negative prohibition in the Torah...If, however, a prohibition is Rabbinic in origin, it is superceded by the consideration of a person's honor in all situations. Although the Torah states [Deuteronomy 17:11]: "Do not deviate from any of the statements they relate to you," this prohibition is superceded by considerations of a person's honor. (Translation from chabad.org)
However, there are authorities who also allow the abrogation of a Biblical law by passively not acting to fulfill a Biblical command- שב ואל תעשה. See the Ran and the Nemukei Yosef on Megilah 3b here. However, even these authorities do not allow the active violation of a Biblical command in cases where human dignity is at stake.
Now, as far as I recall, there are no Rabbinic laws applicable to non-Jews. The only positive command applicable to non-Jews is that of setting up a justice system- a command which is unlikely to conflict with human dignity. Thus, there would never be a situation in which the dignity of a non-Jew would come into conflict with either a Rabbinic prohibition or a Biblical law applicable to them.
It seems to me that כבוד הבריות does not refer to human dignity per se, but human dignity when in conflict with halacha.
It would seem not to apply to dead non-Jews as the gemarah Yerushalmi Shabbos 10:5 indicates you can feed the corpse of a non-Jew to a dog.
תיפתר במת עכו"ם ושאין בו ריח רע והוציאו לכלבו