It will not rid discrimination but it certainly won't contribute to it either. There exists sensible people who are not activists for their views. Politically inactive people who aren't ignorant on these matters but are largely passive. 'I don't see colour' is a quick and easy way to explain your values towards human beings, even if it might not belong in deeper discussions about race like this. It isn't flawed because if nobody cared about race, then any discrimination wouldn't be race related. People walking around not caring about anyones race isn't a bad thing. That doesn't automatically make you completely oblivious to race, or uncomfortable when talking about racial issues either.
Well for one, it's a lie - everyone see's colour, everyone notices when someone is black, white, asian, mixed or whatever.
What you're really trying to say is "I treat everyone the same, regardless of race", which is what everyone should do - there is nothing wrong with calling someone black, white or whatever - you're more likely to be conditioned into thinking that talking about race is a topic that's off limits, it's not. Or you're conditioned into not having to talk about race because white people are the default in any given situation, therefore identifying race is unnecessary, unless it's for a PoC.
For anyone who is 'passive' when it comes to racism, to me, they are worse than the racists, because they see what's happening but they don't care - those are the people who keep racism alive by doing so.
So, if you are explaining your passive views by saying you don't see colour - then yes, you are ignorant and your logic is flawed - Read Martin Luther King's Letter From Birmingham Jail if you'd like any further clarification on the stance of what being passive when it comes to matters like these mean to the very people who are victims of it;
MLK said:
I must confess that over the past few years I have been gravely disappointed with the white moderate. I have almost reached the regrettable conclusion that the Negro's great stumbling block in his stride toward freedom is not the White Citizen's Counciler or the Ku Klux Klanner, but the white moderate, who is more devoted to "order" than to justice; who prefers a negative peace which is the absence of tension to a positive peace which is the presence of justice; who constantly says: "I agree with you in the goal you seek, but I cannot agree with your methods of direct action"; who paternalistically believes he can set the timetable for another man's freedom; who lives by a mythical concept of time and who constantly advises the Negro to wait for a "more convenient season." Shallow understanding from people of good will is more frustrating than absolute misunderstanding from people of ill will. Lukewarm acceptance is much more bewildering than outright rejection.
I had hoped that the white moderate would understand that law and order exist for the purpose of establishing justice and that when they fail in this purpose they become the dangerously structured dams that block the flow of social progress.
The only way we can get to the point where nobody cares about race, is by everyone - especially the passive ones - caring about race, right now. If you walk about not caring about race, what you're doing is ignoring systemic & institutional racism because you are led to believe that treating everybody equally is the only thing that will eradicate racism, sadly it's not. As
@chromepaxos points out, PoC are marginalised & penalised in comparison to white people in almost every aspect of life, from education to environment to housing to employment and more - so saying you don't care about race, while all of this goes on makes you either oblivious, or complicit.