Many of us have racist impulses (and misogynist, homophobic ones, too). I sure AF know I do. It's important that we learn to accept "correction" with grace. All we can do is try. It takes a shit-ton of courage to do what that woman did. A shit-ton.
"I don't see race" is kind of a tell, isn't it? I mean, so much so that Colbert lampooned it.
It's the sort of thing I know I've said, in a different century. I don't think it's ever meant literally: I think the meaning is something like 'I hereby recognize that our relationship has so much going on that this superficial difference between us is as nothing.'* Her response is still the right response to it.
* OK, that's the nice version. The less nice version is 'look at me, focusing on the content of your character just like I'm supposed to! What is the matter with that? What is it you people want anyway?'