If you want to communicate with people, you need to know what they mean by different words. You can't decide for them.

Please read Anthony Eichberger's excellent comment about different types of racism. In practice, this is how the word "racism" has been used for many decades.

If you do succeed in changing the definition to be what you say, "racism" without "bigotry" is cause for hope. The institutions were created because of "bigotry". Without "bigotry", many will fade on their own (all too slowly, perhaps) and others will be easily dismantled. But "bigotry" is a terrible and depressing thing, because personal disdain for others based on the color of their skin or their ancestry provides both reason to harm and reject individuals who you interact with, and everlasting motive to sustain and strengthen and invent new ways to wield power against those you disdain.

So sure, if you want, have it that way; but then "racism" is by far the lesser of two evils. "Bigotry" is hateful and hurtful and yields endless strife; mere "racism" is tragic and awful but we have hope to defeat it, as long as there are not enough "bigots" to sustain it.