What is the term used to define an answer which does not offend anyone?

the word innocuous means not harmful or offensive

I was thinking of anodyne in the sense of "inoffensive", but it has the implication of being dull.

A phrase that has been poured over so all improper implications, offensive ideas, implications of blame, and challenging statements have been removed has been sanitized.

A answer that is politically correct usually implies it won't offend most people. It does not imply anything abut politics.

Diplomatic would fit the bill (as answered above). But I'd say, in a following discussion of your response at the bar among your critics, the word "equivocate" would arise.

Diplomatic would be a suitable word.

Another appropriate term would be tactful.

careful not to offend or upset other people : having or showing tact

mirriam-webster.com

I would call it diplomatic

Diplomatic: Of or concerning diplomacy:

Diplomacy: The art of dealing with people in a sensitive and tactful way

(Definitions from http://www.oxforddictionaries.com/ and not the only definitions of those words)

A neutral answer is generally given not to take sides with any of the party involved:

• belonging to neither side in a controversy: on neutral ground.
• belonging to neither kind; not one thing or the other.

The Free Dictionary

or a diplomatic answer may refer an answer which tries to avoid possible conflicts:

• Using or marked by tact and sensitivity in dealing with others. (AHD)