As far as we know, the Tardis has never had problems with any other companion of the Doctor. So why does she hate Clara so much?
Note: I'm using the feminine form for the Tardis, because in my mind she'll always look and talk like Suranne Jones's humanoid depiction of her in The Doctor's Wife.
The TARDIS exists throughout time and space. This is a difficult concept for linear beings like humans to understand or accept. The TARDIS is able to see the entirety of her own existence through the Time Vortex as well as her relationship to the Doctor, so for her, there are NO SURPRISES despite what we as the watchers of the show are led to believe. The TARDIS is not all-knowing, but the possibilities are within her capabilities to predict with a high degree of accuracy.
The moment when Clara is able to enter the timeline of the Doctor is suspected/known to the TARDIS. Her continued reappearance is a sign something is amiss in the future and the TARDIS is aware of this. The TARDIS does not want iterations of Clara within her because whenever there are, the potential for the event which could lead to the Doctor's eventual dissolution becomes possible.
Thus from the TARDIS' perspective, it is best that Clara not touch the controls, not be in the presence of the Doctor and she is best escorted from the TARDIS and the Time Vortex as quickly as possible. The Doctor may like to think he controls the TARDIS but I suspect she has more control of his actions, positions in space/time and decisions than he is willing to admit.
The greatest danger of time travel is foreknowledge. Knowledge of the timeline of any species means a person could erase the entire species at the moment of their first steps from their primordial ooze with almost no effort. This is what the Great Intelligence hopes to exploit about the Doctor's journey through time This is also what the Silence set out to prevent.
This is what the TimeLords sought to avoid when they began their policing of the Temporal Vortex. It is also what the TimeLords ultimately proposed before they were locked behind the barriers of the Time War by the Doctor.
The season finale shows the ultimate state of the relationships between the Doctor, The TARDIS and Clara in stark detail.
I think “hate” is too strong a word, honestly. The TARDIS is wary of Clara because she recognizes her.
Spoilers from “Asylum of the Daleks”, “The Snowmen”, and “The Name of the Doctor”:
It’s established in “The Name of the Doctor” that a Gallifreyan splinter of Clara nudged the Doctor into choosing the TARDIS he did. It’s not clear how this meshes with the TARDIS’ own statement that she chose the Doctor, but leave that aside for the moment. Chances are also good, though not firmly established, that the TARDIS was at least somewhat aware of Clara’s “impossible” nature and constant recurrence throughout the Doctor’s life, even though the Doctor himself only became aware something was up beginning with “The Snowmen”, when he made the connection between Victorian Clara and Soufflé Girl.
The TARDIS would clearly recognize that only something fairly bizarre and catastrophic could cause Clara to keep recurring like that. Something wibbly-wobbly and timey-wimey. Thus, when Clara began to actually travel with the Doctor, the TARDIS would be understandably nervous that the catastrophe that led to all this was imminent, and thus be not entirely keen on having Clara around.
The TARDIS does not hate Clara.
In episode "HIDE" Clara wins an argument with the TARDIS. She convinces the TARDIS to rescue the Doctor from a pocket universe.
In episode "Journey to the Center of the TARDIS", the TARDIS tries to protect Clara by locking her into the control room.
