Bastila the most annoying? Yeah, probably. Even the romance with her was annoying.
I still don't like Ash and that's not because of her being "racist". It's because in ME1 she tries to sound cool and impress people but instead her dialogue makes me cringe. Still, she would have been okay if BioWare didn't feel the need to make her like poetry. Kinda heavy handed there. Does she absolutely have to have a softer side so she's more appealing to the male audience? Overall, her attitude was too... american.
I am trying to keep her alive in ME1 in my current Renegade playthrough for the first time ever. Not sure how I'll feel about it once I get to pick who dies on Virmire.
She's cheesy, but this whole series is pretty cheesy. Garrus is the king of corny, ham fisted badassery yet nearly everyone seems to like him (myself included). Then again, his softer side was a bit better executed than Ashley's random Tennyson addiciton.
I never saw her as racist. Just skeptical, which is a trait I value.
But then that was badly undercut by her theism, and that's why I didn't like her.
She's hardly the only theist on the crew, one of her conversations in ME1 just happens to cover it. Garrus refers to the spirits freqently, Wrex makes religious references (the Void). Liara's catchphrase includes a reference to a deity (by the Goddess). Nevermind when you get to ME2 and you have Thane's very in your face religiosity, yet more Goddess from Samara, along with Modin's spiritual repentance being a theme brought up in his loyalty mission.