Is it a word itself that is offensive, or the idea that the word conveys?

A word is made up to mean something therefore the word is not the offensive party. A child who means no harm can say a WORD that can still come out offensive therefore the way the word is conveyed is offensive so then that would make the idea that the word conveys the party that is truly offensive.

i think it ends up being a combination of the two but mostly the latter

The idea the word conveys.

Good question.

The idea

A word is a symbol of a picture" we have of a reality.
The picture is also a symbol of the reality.
So, a word is a symbol of a symbol and thereby already two steps removed from reality.
The power "we give" symbols is wherein lies the problem.
The power is ours to do with as we choose and many of us choose to be offended by these symbols which are not the reality.

It's is what the word refers to, A rose by any other name would smell just as sweet,
A pile of crap by any other name would still be a pile of crap

Definitely, it is the idea the word conveys, at least in almost all instances. Albeit, the word gargle, just saying it, is mildy offensive...

Words are powerful and it all depends on how one understands the word to make it offensive or not.

The way that word is perceived..

holy Sh!t
is that offensive or the idea that it conveys?
thats up to you to decide