And surely this is a hinderance. What should I do? I practice just sitting. And I think I am in equanimity stage. Fairly certain.

What does stream entry mean to you?

Note "thinking" "craving" when obsessively thinking about something.

It means being something that I am not...

Silly...

How about asking the question this way: what are you dissatisfied with about the way things are ?  Try to be as specific and localized as possible - what sensation or thought arises that you want to stop arising ?

stream entry just shows you that everything is actually fine as it is.   

...or that you have always been enlightened.

Stream Entry is guaranteed to be different than what you think it is, and in a strange way, familiar.

You CAN'T be obsessed with it, since you have no idea what it is, but you CAN be grasping at relieving your suffering. When this happens, don't try NOT to grasp, but notice that there is grasping, or a train of thoughts that forms around your ideas of what Stream Entry is. Surrender that grasping. Let the thoughts dissapate.

I want to eradicate wanting. Paradoxical I know. But once wanting (wanting stream entry) arises I have an aversion to it. Stories start to play in my head about how I am a bad Zen student etc.

That is the way the mind works - it sounds stories and gives them a sensation soundtrack.  The mind reads the sensations as telling it how important the story is and how bad or good your situation in that story is.  The whole game is to let all that stuff just pass through the mind like clouds through the sky - or like shit through a goose !  

None one of us have any control over the stream of thoughts an sensations that arise - our only "choice" is whether to care about them or not.

do you do metta mediation?  Do you listen to reggae?  Trying just loving everyone and jamming some - the mind nonsense will take care of itself. 

"I am obsessed with stream entry"

It's better to be obsessed with consistent daily practice and wise use of retreats.

https://www.youtube.com/watch?v=4BjKS1-vjPs