As far as I can tell, there are effectively two different definitions of racism that are frequently conflated, causing misunderstanding:
The common definition of racism appears to be that racism is the practice of using specific words and phrases that are considered offensive to a specific group of people - in essence, a kind of hyper-rudeness that only affects a minority among the population.
Another, less common, definition of racism is so-called "structural racism", where racism is seen as a state of society that is the result of a fundamental imbalance of social status and political influence among certain population groups - essentially a certain type of power relation that exists throughout society, and is often maintained by practices that are not intended to be bigoted or racist at all.
Which one of the two do you believe applies here?
I'm not sure that either would apply. These are the two main definitions from Webster's:
Racism | Definition of Racism by Merriam-Webster (merriam-webster.com)
a belief that race is a fundamental determinant of human traits and capacities and that racial differences produce an inherent superiority of a particular race
the systemic oppression of a racial group to the social, economic, and political advantage of another
The first definition indicates "a belief that race is a fundamental determinant of human traits and capacities." Anyone can have this specific belief, yet it might manifest in different ways. I remember @Audie would sometimes speak of the "White Liberal Savior Industrial Complex," somewhat jokingly, but I think most of us here knew what she was talking about. There's a certain condescension that comes into this. Essentially, this training program is a white person explaining that being "white" amounts to a certain set of behaviors and personality traits. It seems like it's directed towards other whites, but that's not entirely clear. Either way, the author of this training program is, by her own definitions and standards, "acting white" in the process of encouraging others to "be less white."
Thinking on that, it's not really a double standard, but the same standard, and that's the problem. The bottom line is that the same structure (as you note above regarding "structural racism") is still intact and operating. The way our society has dealt with racism has been mainly at a surface level, focusing on the superficial and symbolic. As you say, it comes down to saying certain words and phrases, and if someone says the wrong thing, then their career and reputation go straight into the toilet. But the structure still remains. Nobody wants to change the structure. Nobody wants to rock the boat.