Adjective or noun for a person who takes offence deliberately or insincerely

There are several words like quarrelsome, argumentative & confrontational (may be more) but the closest I can find to your (example) scenario is antagonistic. (See the example from ODO below which is pretty close to yours).

ODO:

antagonistic

ADJECTIVE

1 Showing or feeling active opposition or hostility towards someone or something:

‘He was rude and antagonistic to my friends, kept picking arguments and was often deliberately provocative, manipulating people into tense arguments.’

Alice is a stirrer.

(Aka a shit stirrer or pot stirrer.)

Perhaps this is too general since it is not limited to the incincere offense-seeking

Stirrer

British informal. A person who deliberately causes trouble between others by spreading rumours or gossip.
[...].
‘Unlike Walter, he is a stirrer, a deliberately provocative commentator and a freewheeling iconoclast, infamous for his relentless critique of the American government and military.’
OD

Although not directly related to taking offense, the two words that immediately came to mind were

Argumentative

adjective ​

often arguing or wanting to argue:

and...

Contrarian

ADJECTIVE

Opposing or rejecting popular opinion or current practice:

Contrarian fits less, but it summons an image of someone who wants to or is looking for an excuse to disagree with someone for one reason or another.

Alice is being intentionally arguementative or contrarian as a means of expressing her dislike of Bob.