A word or idiom for being offended for someone else

Solution 1:

I would suggest vicariously offended.

Vicarious:

performed, exercised, received, or suffered in place of another

I've found a few published uses of the phrase:

Use 1:

... making their living by being vicariously offended ...

Use 2:

There's a tendency in this country for people to be vicariously offended

Solution 2:

A term I have seen used more recently is Professionally Offended or Professionally Outraged.

This is used to describe someone who takes offense at something on behalf of the supposedly offended party, usually on Twitter.

Phillip Schofield has described Twitter as "the land of the professionally outraged".

DigitalSpy

Solution 3:

The idiom, take something personally, may fit in this scenario. Definition:

to interpret a remark or action as directed against oneself and be upset or offended by it, even if that was not the speaker's intention.

Example:

"I took it personally when he yelled at the class."

(The Oxford Pocket Dictionary of Current English)