Unoffendable

[PussyCat]

not caring [one way] or the other about a subject, [regardless] of how [offensive] it my be.

[Oralee]

Incapable of being offended; unlikely to take offence.

[Kit]

Means the person you are speaking with is capable of listening to the entire conversation without becoming offended.
Example;
I like to have sex with my dog.
I enjoy having sex with my child.
I enjoy shitting on colored people.
Please keep in mind that unoffendable is a state of mind, that is neither PC or racist, in todays society. I can be [unoffendable], WITHOUT enjoying the examples provided.
You can tell an unoffendable person about bodily fluids, [toenail clippings], or a severe rash in your private areas.
Most doctors that treat patients must have some form of this word [embedded] into their brains to fulfill their daily duties.