Difficulty understanding redox in terms of hydrogen and oxygen transfer?
You are quite right, those rules of thumb are not always valid.

To be precise, the "adding hydrogen = reduction" rule only works for elements more electronegative than hydrogen, and the "adding oxygen = oxidation" rule only works for elements less electronegative than oxygen. For example, sodium is less electronegative than hydrogen, and as such adding hydrogen to sodium ($\ce{Na -&gt; NaH}$) is in fact an oxidation of sodium from 0 to +1.

However, I wouldn't be so quick to limit their application to "organic chemistry". The elements that are less electronegative than hydrogen are just the metals, and the only element more electronegative than oxygen is fluorine.

Therefore, adding oxygen to chlorine is an oxidation, although the oxides or oxoanions of chlorine are classified under inorganic chemistry. Likewise, nearly the entirety of the p-block obeys these rules (except for Group 13). Think about germanium, arsenic, etc.. those are undoubtedly not "organic chemistry".