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

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)

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

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.

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

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.

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

the word innocuous means not harmful or offensive