Stop saying "I'm racist." I mean, unless you are.
There are people who believe hateful things about people of different races. There are people who act on that hatred. There are people who commit violence because of them. We have a powerful, succinct label for people of such moral depravity: racists.
Your approach would free these people from much of the fully-deserved scorn that comes their way, because, to co-opt a phrase from the Incredibles, when everyone is a racist, no-one will be.
Don't give shelter to these views by trying to water down the term. Don't call yourself a racist unless you are, and don't encourage other people to do it either.
If you want to acknowledge that you have subconsciously (or consciously) incorporated societal racial stereotypes, like most every one has...then...say that.
If you want to accept that you benefit from institutional practices that enable you while impeding others of different races, awesome. It's true, you do very likely benefit from such things if you're white. And it's not fair, and it should change, and you shouldn't feel bad about it unless you're impeding the change--just help make it happen.
But don't use your personal journey of growth and acceptance and change and signaling to others about this process as a way to shield actual racists from appropriately severe scorn. Remember, as you said: it's not about you.
Only if you actually carry substantial amounts of racial bigotry (especially if you act on it) should you say "I am a racist".
Then, if you do--well, thank you, at least you're being honest. This is, perhaps, a first step to changing.
Addendum added in edit: if your social group requires you to say “I am racist” in order to belong despite you not having significant personal racial bigotry, then you may need to make an individual choice about whether your inclusion in the group is more important than preserving a powerful anti-racist vocabulary. It’s still unwise to advocate that others do this, for the reasons I state above. If their social groups require that they say “I am racist”, they’ll know it when it happens and they can make their own decisions.