If a house style outlines that foreign terms should be italicised, how strictly should this be applied to common terms taken from, say, French that everyone is more than familiar with? Italicising café seems quite drastic, so what about words such as crèche? I'm not sure exactly where to draw the line between foreign and English considering the number of French words and terms borrowed by modern English.
The house dictionary should "draw that line" for the entire organisation!
Anything not listed in your house dictionary is foreign and needs italics.
You need to look at the explanatory information provided at the front or back of that dictionary. It will contain - tell your boss to buy another dictionary if it does not - an explanation of how it displays expressions which (a) exist in another language but not (yet) in English, or (b) now exist in English but are derived from another language.
Type (a) should be in italics, type (b) should not.
Note, there is no right or wrong about whether a word has fully arrived in English, yet? The decisions by dictionaries are not quite arbitrary; they are based on the analysis by the compilers of the dictionary of the way they are being used by speakers of English.
The reason for reliance on a dictionary is not right or wrong, it is to have one source that everybody in the organisation uses to ensure the same expression is always shown with the same style. It would be inconsistency in uses which may make the organisation appear sloppy, not the various choices made to show expressions with one style or the other.