Learn English – a word for when you pass the responsibility of something to someone or something else

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

One obvious word is simply unaccountable:

[Merriam-Webster]

2 : not to be called to account : not responsible

The only other single word I can think of—although it has a broader meaning than you might like—is

Exempt:

[Merriam-Webster]

2 : free or released from some liability or requirement to which others are subject • was exempt from jury duty • the estate was exempt from taxes

Of course, there are also some very specific contextual phrases. For instance, diplomatic immunity.