I am curious what the definitions of "insubordinate" and "inappropriate" are in the context of workplace behaviors.
I think this may be a bit dependent to interpretation, but venturing to answer what you ask we should analyze the definitions of those words first:
Insubordinate: not submitting to authority; disobedient.
Inappropriate: not appropriate; not proper or suitable.
Based on these, we can say that an insubordinate is someone who defies or neglects authority (managers, leads, etc.), perhaps by making their own calls despite official courses of action to be taken. This should be really universal across many workplaces, and it is usually clear when a case of insubordination takes place.
We can also say that something inappropriate is something that does not fit to the code of conduct of a specific company, or well to the expected behavior or professional interaction between any fellow worker. Saying impolite/rude things, or mixing personal situations with your job are example of inappropriate behaviors across many companies.
I also suggest you contact your HR department, or whomever corresponds, to inquire about the specific cases that are considered insubordination or inappropriate for your current company, so you are better prepared to interact professionally in such place.