Are there official criteria what undergraduate programs in different majors must cover at US schools?
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.