As you’re making an assumption about a past event, both are grammatically correct. However, conditionnel stresses better the idea of hypothesis.

Let me explain with your example :

• Sa fierté aurait été blessée : you’re making an assumption, but you want to stress neutrality. For instance, in a journalistic style, it implies that you take a step back from this piece of information.
• Sa fierté aura été blessée : you’re also making an assumption about a past fact, and you’re implying that this must have happened.

As you’re asking a question, you may not be sure about what really happened, and conditionnel conveys better this idea of uncertainty.

Saying futur antérieur can mean “the possibility of the past” is imho not correct or at least ambiguous, futur antérieur can be used to describe an event that could (or might) have taken place in the past, we just are not sure whether it has, it’s just a possibility we consider but cannot guarantee.

The past conditional, like the present conditional, gives information on a past event about which the accuracy cannot be guaranteed, it is one of its prime uses.

Both futur antérieur and contionnel passé are used to make assumptions regarding past events about which the accuracy cannot be guaranteed. The only difference I can see between

• Il a donc quitté le village après ça ? Sa fierté aura-t-elle été blessée ?

and

• Il a donc quitté le village après ça ? Sa fierté aurait-elle été blessée ?

is in the degree of uncertainty expressed. Using the indicative (futur antérieur) shows the speaker has less doubts about the action actually taking place than when using the conditional (conditionnel passé).