What is a synonym for "necessary kindness"?

I'm currently searching for a word for what I call "necessary kindness".

Let's say there are two people who normally don't get along with each other. When they are together in public, however, they treat each other with politeness and respect, according to social norms.

By the way, the word doesn't necessarily have to have a negative connotation, nor does it need to convey rudeness or offensiveness.

EDIT

I would also like to be able to use a word in a situation such as when a friend or acquaintance compliments you.

"You look nice today!" "I appreciate your ______ but that's not necessary"

In that case, the 2 people aren't "tolerating" each other just being unnecessarily polite.

Solution 1:

Consider civility, defined as

courtesy; politeness (Dictionary.com)

The people of your example can be said to be showing civility to one another, or being civil to one another.

The reason I think this word is a good fit in the situation you describe is because

Civility comes from the Latin word civilis, meaning "relating to public life, befitting a citizen," (Vocabulary.com)

As such, the word connotes kind behavior and attitude in public, not necessarily in the privacy of one's own home or mind. The kindness is necessary in public, but not necessary elsewhere.

Solution 2:

Perfunctory - adjective - performed merely as a routine duty; hasty and superficial:

http://www.dictionary.com/browse/perfunctory