If you don't respect her and are embarrassed by her, let her go so she can find someone who isn't. She's not going to change and she shouldn't feel she has to.

Her biggest compliment of me is that I have accepted her in ways that no one else ever has

But you don't actually seem to accept her, leaving me wondering if that's just a facade. You can either actually accept her for the way she is, or you can let her go. Do NOT make her feel like she needs to change. Nobody should have to study and pass an intelligence test to keep their relationship.

How do I not feel embarrassed when she's acting a bit clueless in public?

I think this is kind of just who you are. Just like that's who she is. Either you find a way to change and stop entertaining those thoughts, or you end it.