Biochem, when offered as an undergrad program, is offered through the biology department and has a number of standard biology department requirements that would be elective at best for chemistry undergrads. Biochem majors also take orgo following gen chem, just like chemistry majors.
I don’t know what “touchy-feely” means in this context, but “chem except you take orgo almost immediately” does not match with my experience at all.
I have no idea what bringing up ChemE has to do with anything: undergrad ChemE has little to do with chemistry and a lot to do with continuum mechanics and steam tables. It's common for engineering students to do their natural sciences classwork (it isn't called "earth sciences", that is something else) together along with major students.