If you don't agree to, refuse to follow, or ignore McDonald's terms, they will refuse to allow you to operate using their brand (ie. franchise).

There is no law that forces McDonald's to extend you a franchise license. It's their right to run their brand how they want.

Part of the franchise contract would be an agreement to use their approved vendor/parts list.

I agree with you that this idea makes no sense. But I think your argument doesn't make sense. McDonalds can't deny someone a franchise license on the basis of them being black. They are compelled to not consider race when offering franchise licenses regardless of whether or not they'd like to. (I say that because, as far as I know, having non-race-blind preferences on who to do business with is not a crime, only acting on it is.) I see no reason a similar law couldn't theoretically also force them to not consider whether owners modify their ice cream machines.

Being Black and refusing to follow a franchise agreement are very different things, no?

If some law passed and McDondald's was going to lose control of franchises, consistency and their brand, they'd probably pivot to a mostly or entirely corporate-owned/operated model.

However, it's unreasonable to assert a franchise should be able to use whatever devices, machines, standards and consistency they want... which is what is being advocated here it seems.

As an aside, your example about refusing to sell a license to someone based entirely on the color of their skin would be quite difficult to prove and enforce. I'm not advocating for anything, just pointing out they can deny a license for pretty much any reason, or no reason, and nobody would be able to compel them otherwise. It is their brand, and nobody has a right to operate using that brand unless McDondald's allows it. That's the entire point of a franchise - use someone else's brand.