I didn't say "invented" either, I said "made up" - I used the exact same wording you did. Don't put words in my mouth, it's unhygienic. And I would say that of all the foods to pick for the analogy, going straight for M&Ms in particular is, shall we say, telling.
"FBI crime stats" is, in fact a good critique. If we accept bigotry against immigrants is unjustified because their crime stats are low, logically, we are forced to accept that if they were high, bigotry would be justified, which is the "FBI stats" argument. Now, I realize I might be on the fringe here, but I would like to take the stance that bigotry is inherently unjustified, regardless of what stats someone can dig up. Crime stats, historical oppression, financial disadvantage, and other PMC buzzwords do not matter. Either we agree that a person, an actual, living, breathing, human being with feelings, hopes, and dreams, can be pre-judged based their birth (prejudice: prae- “before” + iūdicium “judgment”) , or they can't. And I am of the radical, extremist stance that prejudice is wrong, inherently.
And what the fuck do bears have to do with any of this?
I'm not strawmanning anything, the M&M argument itself is a justification for bigotry. It's not shutting down the conversation, that is the conversation being had. The M&M argument isn't about helping people, it's a justification for prejudice and is to be rejected out of hand regardless of what demographic it's targeting or what justification it tenders, because human beings aren't fungible commodities. Read the articles I linked. Crime stats do not need context, because they do not matter at all.
How do you respond to M&Ming Japanese-American internment? After all, not all of them are traitors, but one poison M&M... And in response, do you say "well, if you look at the data, the average Japanese-American was actually..."? No, you reject the argument out of hand, because people are innocent until proven guilty. How do you respond to M&Ming vagrancy? Do you dig up data on shelters and talk about mental health? No, you reject the premise, because freedom shouldn't be contingent on property ownership. How about migrants? Do you waste time proving that actually they're all nice people who are worthy of help? No, you reject the argument, because people in need should be helped.
Incidentally, inherentness is also irrelevant. The M&M argument doesn't claim poison is inherent to M&Ms. You can just as easily make the argument that you know full well that ...m e n... aren't inherently violent, it's just that the crime stats very clearly show that they, as a demographic, have certain tendencies, and while you sympathize with them, and would like nothing more to help them overcome the circumstances, probably cultural, that are surely to blame for them being that way, the data is what it is, and you just don't feel comfortable working/socializing/sharing an elevator/being in the same bar/seeing them in the neighborhood, and, I mean, for all they complain, the back of the bus is still on the same bus so I don't get...
I realize nobody thinks of themselves as a bigot, and I know reexamining one's own biases is not pleasant, but it is a necessary step for growth.