The Federal Archives of Germany have published an official document called "The list of Jewish Residents in the German Reich 1933-1945"*. The document states verbatim:
“The two population censuses dated 16 June 1933 and 17 May 1939 give
some clues about the number of Jewish residents, where it should be
taken into account, though, that both the territorial conditions as
well as the categorization of being Jewish (in 1933 purely seen as
religion, in 1939 according to racial aspects) had
—The Federal Archives. Henceforth: Das Bundesarchiv (2011), p.3
I interpret the second question as asking "Did the minorities believe that the intentions of the Nazis were sincere?". As I alluded to earlier, the 1933 census form uses the classification of Jews based on religion. This is in no regards different from the 1925 census (Das Bundesarchiv, 2016, April 27). One is then left to consider, that the only observable change for a person, belonging to a minority in Germany in 1933, concerns the impression of the government at the date of the census: June 16 (cf. Das Bundesarchiv, 2011).
In no uncertain terms was the persecution of Jews a covert procedure. Pictures from Berlin on April 1, 1933, show German-English signs with the words:
"Germans defend yourselves against jewish [sic!] atrocity propaganda.
Buy only at German shops"
—Wrocklage, 2006/2015, p.5
These signs were carried by the SA, Sturmabteilung (lit. "Storm Department"), the paramilitary force of the Nazi party.
While this is an example of evidence for the perception among minorities, let us consider other Germans during this time. The German freedom of press was severely limited on January 30, 1933, according to a journalist who attended the national media conferences between 1919 and 1944 (Wrocklage, 2006/2015). The manipulation of the people was intentional and the source of information was centralized and uniform due to state control (Wrocklage, 2006/2015).
Was the census an instrument of realizing the holocaust? Yes. Has it been used in accounting for how many Jews lost their lives during the holocaust? I will leave the latter answer as an exercise to the historically informed reader. As a German resident I can say that it is indeed illegal in Germany to downplay the extent of the atrocities. Questioning the authenticity of such official reports is a practice that I condemn.
Were the Germans being fooled by the Nazi government? Yes, but there were exceptions and most likely among "the minorities".
Essay on the Relevance for the Australian Census
Having answered the question by exposing the facts, I now turn to the essay, since the question has been asked in the context of the Australian census—to which one can have but opinions, whether informed or not. The history of statistics is sadly plagued with eugenicists (e.g. Francis Galton, R. A. Fisher, and Karl Pearson). Today, however, statistics is the hallmark of science, from doctors and psychologist to astronomers and quantum physicists, it is a ubiquitous instrument. Increasingly, data is becoming open. Methods and procedures are becoming open. Some governments have web pages, others shut the internet down.
Informed consent is the guiding ethical principle for human research. It is a descendant principle from the Nuremberg Code (https://history.nih.gov/research/downloads/nuremberg.pdf) and the Declaration of Helsinki - in the wake of the war. The crimes of the Nazis lead to increased ethical awareness, but insufficiently so. The Tuskegee syphilis experiment was carried out by the U.S. Public Health Service (involving the minority of African-American heritage) and lasted until 1972, but still resonates this decade.
The way forward is to perform a cost benefit analysis for the people. Perhaps stronger encryption laws for personal data are required to protect privacy. Perhaps ethnicity should not be registered. Perhaps the relationship between certain diseases and socioeconomic status can help research and thus society forward. What are the pros and cons of census versus privacy? In the case of the 1933 and 1939 censuses, they were also used in modern times to identify the rightful owners of Jewish companies and properties that were attained under the Nazi rule, as was described by Das Bundesarchiv (2011).
Finally, a trained skeptic should recognize when comparisons with Nazism are relevant and when they are nothing but a fallacy: reductio ad Hitlerum. I strongly believe, that the often occurring comparisons with Nazi Germany do not only downplay the uniqueness of the holocaust - the worst genocide of modern times - but also belittle those with a heritage of suffering.
*Concerning the title of the document, it is not to be confused with the list itself. It provides a detailed description of the register, its sources, and its purpose. Concerning the author of the document. Nicolai M. Zimmerman refers to an employee at said institution. The document properties state the author as "Das Bundesarchiv" and the document is issued by Das Bundesarchiv. "The Federal Archives have the legal responsibility of permanently preserving the federal archival documents and making them available for use." (Das Bundesarchiv, 15.06.2013 12:20)
Das Bundesarchiv (2011). (Nicolai M. Zimmerman, Ed.) The list of Jewish Residents in the German Reich 1933-1945. Retrieved from http://www.bundesarchiv.de/imperia/md/content/abteilungen/abtr/residentenliste_english.pdf——German version: https://www.bundesarchiv.de/imperia/md/content/abteilungen/abtr/internet_zu_residentenliste_1_.pdf
Das Bundesarchiv (2013, July 15, 12:20). Responsibilities. Retrieved from https://www.bundesarchiv.de/bundesarchiv/aufgaben/index.html.en——German version: https://www.bundesarchiv.de/bundesarchiv/aufgaben/index.html.de
Das Bundesarchiv (2016, April 27). Gedenkbuch. [Memorial Book]. https://www.bundesarchiv.de/gedenkbuch/einfuehrung.html.en?page=2
Wrocklage, U. (2006). [Media Portrayal around 1933. Continuity or break?] Presse und Bildberichterstattung um 1933. Kontinuität oder Bruch?, in: Ulrich Rüter (Ed.), "Think while you shoot". [Martin Munkacsi and the modern picture journalism] Martin Munkacsi und der moderne Bildjournalismus. (pp. 74-85). Hamburg: ConferencePoint. Reprint in: [Studies in Contemporary History] Zeithistorische Forschungen (Eds. Sabrow, M., & Kleßmann, C.). (2015) http://www.zeithistorische-forschungen.de/sites/default/files/medien/material/2015-2/Wrocklage_2006.pdf