The Moravian censuses from 1857-1910 are now online in beta form at https://www.mza.cz/scitacioper
The website is completely in Czech but easily translated using GoogleTranslate or DeepL.
The census books are in German or bilingual German/Czech and include columns such as birthdate, marital status, birthplace, etc. Apparently in later years information such as disabilities was also recorded.
FamilySearch digitized some of the census books a few years ago (but I don't know if they are indexing them) and the archives digitized the rest in the last 2 years. The 1921 census was also digitized but is not online yet because of privacy regulations.
This information was posted today on the discussion list of GenTeam.eu. The list covers the entire Austrian-Hungarian empire so if you are interested in the region it might be worth it to you to subscribe. The posts are usually in German, but most of the regular posters speak good English. The GenTeam.eu website has a lot of information about Jewish communities so is also worth a visit. I have no affiliation with GenTeam- I just find the website and discussion list very useful.
Megan Lewis, reference librarian, United States Holocaust Memorial Museum