Black immigrants in the US have roughly the same level of financial success as Asian immigrants, they are just a much smaller portion of black Americans than Asian immigrants are of Asian Americans. The real difference is between immigrants and non-immigrants, not between black and Asian people.
Also, it's untrue that immigration law applies equally to all races. There are many aspects of immigration law that are different based on national origin. People from India and China are excluded from many ways of immigrating except for work visas.
Do you agree that it's best to promote a message of "don't blame others for your failures" over a message of "your life is mostly dictated by luck"? I don't see how you could argue that the latter is better than the former.
And I really won't change my mind on this notion, given that my parents started up poor in Brazil and worked their way up to provide me with a reasonably good life, way better than the ones they had. And the main thing that enabled them to do that was their own mindset about life and just a lot of hard work.
The same applies to many other people I know, and the opposite also applies to many other people I know. There are people who simply don't work as hard, or don't pay enough attention to spot opportunities, or aren't financially responsible, or are alcoholics, or any other number of problems that are self-made. Those people keep themselves trapped in a cycle of poverty through their own actions, not anyone else's.
Isn't part of the whole immigration debate in America the fact that Latinos find it easy to illegally immigrate here? Asians literally have whole oceans to cross to get here. Many Latinos can get on a truck and just drive across the border.
You also can see huge income differences between African immigrants and native-born African-Americans. This has less to do with mindset and more to do with the selection bias TheCoelacanth mentioned. Immigrants from Asia, India, Africa, etc. will be more financial successful because they are deliberately selected for.
I think you can't discount the fact that Asians simply have a better mindset that focuses on hard work more than other groups, which explains at least part of their success. And it's really not a surprise to think that if you value hard work and you act on that value by working hard, you will be rewarded. There's no need to make up excuses by blaming systemic racism or any other sort of external influence that doesn't play as much of a role in your life as your own effort will.