I'm a white guy that thinks about this question pretty frequently, and I really think we need to reframe the discussion away from racism as this singular, monolithic thing that a person "is" or "isn't", and instead treating racism as a multifaceted spectrum that comes in varying, often overlapping forms--ignorance, apathy, hostility, systemic, insecurity, subconscious expectations, and so on.
In general, it's not a binary thing; a person can say or think racist things without being a hardcore, dyed-in-the-wool white supremacist. Some people are amenable to reason and are willing to change their behavior if you simply explain the problem to them. Others will clam up and become childishly defensive at even the slightest whiff of talking about race. Different causes will require different solutions.
One lesson I've learned the past few years is that it's often more productive to look at the implications and assumptions underlying a person's argument more than the argument itself. This applies to a lot of things, but this is especially true when talking about racism, where so much is a product of subtle, unspoken expectations.
A perfect example is the ongoing talking point among Trump supporters that they're being unfairly smeared as "false racists" by the Left, who essentially invented racism for the sole purpose of making Republicans look bad.
Now, here's the thing: There is a gray area where an otherwise good person can say something mildly ignorant, be corrected, apologize, and everyone moves on with their lives. Nobody's perfect and we all have our blind spots.
This is the crux of the "mislabeled racist" myth--the person complaining about it is essentially arguing that they made some extremely minor breach of etiquette (conveniently, they never specify exactly *what* they said that's so offensive) and are being horribly persecuted for not being a mind reader.
The total lack of specifics makes this point very hard to argue on its face, because they can keep vaguely implying that whatever offensive thing they said was minor and petty.
Except...why haven't you changed your behavior? If you truly "don't have a racist bone in your body," wouldn't you want to ask the people you offended what you did wrong so you can stop doing it? Isn't that kind of how a healthy human brain with functioning people skills works?
Why are you framing yourself as the victim? Why doesn't the fact that *you're being "falsely" accused of racism on a regular basis* ring any alarm bells?
It's the premise. The selfishness. The reflexive assumption that, as a white person, you are automatically an authority on all issues, especially race, regardless of your knowledge (or lack thereof) on the topic.
I say this because there IS an important conversation to be had about where we draw the line between "acceptable ignorance" (i.e. something very specific a person of average intelligence and empathy probably wouldn't consider or be aware of) and "unacceptable ignorance (where the person's lack of knowledge is a product of apathy so extreme it becomes dehumanizing).
It's easy to point to a very cut-and-dry example of racism like the murder of George Floyd, but being able to better clarify our shared moral accountability in this grey area will go a long way in coming up with lasting ways we can change our dialogue about race in America for the better.
Until then, passive-aggressive cowards will cloak themselves in ambiguity and innuendo to shield themselves from the consequences of their actions.