The two long sections of Parashat Emor deal with the laws of the kohanim and those of the moadim (Jewish holidays). In between, there is a short section that mentions three mitzvot: not bringing a newborn animal as a korban; not slaughtering a mother and child animal in one day; and eating a korban toda on the day it was brought. Then the Torah gives general instructions not to defame His Name and to sanctify Hashem’s Name, for He took us out of Egypt to be our G-d (Vayikra 22: 27-33).
Commentators disagree as to the audience this section is addressed to. The Ibn Ezra sees it as a continuation of instructions to the kohanim, arguing that the content applies primarily to them and that no statement addresses the matter to the whole nation. However, Chazal saw at least the last p’sukim as the source for the prohibition for all Jews not to desecrate Hashem and, to the contrary, to be willing to give their lives rather than publicly violate the Torah (see Rashi to 23:32; Sefer Hachinuch 296).
Let us explore other indications to the latter approach. The kriat hatorah on one of the days of Pesach and Sukkot consists of our parasha’s discussion of the moadim. Yet, it starts with the p’sukim in question, after skipping the lengthy section addressed to the kohanim. In regard to content, not only the words "I will be sanctified in the midst of Bnei Yisrael" but also the idea that we should do so because Hashem took us out of Egypt seem addressed to the entire nation, not the kohanim specifically.
Finally, let’s look at the introduction to the p’sukim to see if the Torah labels the recipient. The entire section that is clearly addressed to kohanim is broken up into pieces that start with lines like "Speak to Aharon and his sons" or "Speak to the kohanim." In contrast, the p’sukim in question begin with the standard opening of "Vayedaber Hashem el Moshe leimor." On one hand this seems like a strong indication that the addressee is no longer the kohanim but all of Bnei Yisrael, the Torah’s standard audience. On the other hand, the Ibn Ezra says that from the fact that there is not an explicit reference to "Speak to the Sons of Israel" as the next section (moadim) has, we can infer that the audience has not changed from the kohanim.
When considering the ambiguous nature of the introductory statement, one can’t help but consider that the ambiguity is intentional and turns the section into a bridge of sorts. The message is apparently as follows. Just as kohanim have special responsibilities and obligations because of the special status they hold within the nation, so too are there elements of all Jews’ behavior that stem from the fact that, vis a vis the nations of the world, we are to be "a kingdom of priests and a holy nation." In this context, we must at times go beyond the normal rules and be willing to sacrifice our lives because our high status demands this of us.