What noun do we have that means 'offendableness' or 'offendability' (tendency) or that means 'offendedness' (state)?
Solution 1:
Being thin skinned is to be easily offended. This usage is idiomatic.
Emotionally susceptible to or unable to ignore the verbal attacks or criticisms of others.
As in:
You can't be thin-skinned if you want to be in the entertainment industry.
Solution 2:
Irascible: having or showing a tendency to be easily angered.
Irascibility: The more you 'ave, the less you 'are
Solution 3:
This state could be called touchy:
Tending to take offense with slight cause; oversensitive.