Are there official criteria what undergraduate programs in different majors must cover at US schools? I recently found that the largest share of students in program X at my school do not need to take classes on topic ABC, even though topic ABC is considered as critical and fundamental by virtually everybody in the field. (Think of physics but no mechanics class)
In fact, I can't believe anybody would give them accreditation without making ABC a required topic.
Which makes me wonder: Are there any official criteria in the US about what a majors in X, Y, or Z must cover in the United States? Can a school just decide arbitrarily what needs to be covered in their majors? Can those criteria be seen in public?
This is an addition to the other answers.
Most professional bodies publish guidelines on what majors in their fields should include.  For example, a joint committee of the ACM (Association for Computing Machinery) and IEEE (Institute for Electrical and Electronics Engineers) publish guidelines for what should be part of a computer science major.  The MAA (Mathematical Association of America) publish guidelines on what should be part of a mathematics major.
In some cases, these guidelines are quite specific.  In others, they are much more vague.  The ACM guidelines are fairly specific.  For largely political reasons, the MAA guidelines are fairly vague.  (This is because departments at universities with more academically capable student bodies and or PhD programs want guidelines that would prepare students for graduate school, while departments at universities with less academically capable student bodies know that they have no students capable of completing such a program of study.)
These are guidelines, not requirements, but they are reasonably influential because many professors do pay attention to them.  In addition, as mentioned above, in certain subjects, there is subject specific accreditation that may impose requirements on the departments involved.