A lot of people say that the colorblind approach to race is racist. I can understand how people can take it that way - but misconstruing people's words on purpose isn't going to help.
When people say that saying "I don't see race" is racist, the main argument is that it means the person is ignoring racism. By not seeing race, the person ignores that people of other races don't have the same opportunities as they do, or that they are ignoring they can be discriminated against because of their color. I understand this argument, and it has a point. The biggest problem I see with it is that it can be taking the phrase out of context and not paying attention to what people actually mean by the phrase, and most of the time it is purposefully ignoring the intended meaning of the phrase.
What people actually mean when they say "I don't see race" is that they want to treat all people equally. They aren't saying that people of other races are just as well off, or that they don't want to help them when they can. They are saying that they want to treat everybody well, regardless of race. That person personally wants to treat other races the same way they treat their own race, which is equality. They try to treat all people well.
This phrase is extremely well intentioned. In reality, I don't even hear it said by younger people. The people who say it are usually older, and are honestly trying to treat all people equally and not be racist themselves, and they use the phrase to say they actively try to not be racist. They really aren't ignoring race, they just don't think it should impact how they treat other races. They understand racism exists, they want to not be personally racist and this is their way of saying that. Instead of yelling at them that it's racist to say that, intention and the meaning behind the phrase should be considered.
My grandma said to me once that she doesn't see color. A Hispanic family's car broke down in front of my grandparents' house, and she was a bit disheartened that they seemed almost afraid when she approached them, and still distrustful even after talking to them. She told me after they were able to leave that she was sad that they didn't trust her because she doesn't see race or color, and she didn't understand why everybody can't treat everybody well. My grandma isn't racist for using "I don't see color" as a way to specifically say she isn't racist.
I feel like a lot of people who say that it's racist to say "I don't see color" know that blatantly ignoring race is not what those people are doing. They know that those people mean they want to treat everybody equally. They know those people would probably give other races a job if they were most qualified, those people would probably not automatically believe everybody of another race is bad, those people would probably not withhold anything from another race for any reason. They just want to feel like they're doing something by telling people they're racist for a phrase intended to not be racist. But purposefully distorting the words people say divides, and causes more opposition than it gets rid of.