If she meant "Muslim" (or some other Asian religion that doesn't endorse alcohol) rather than "Asian person" of course she was being racist. She was saying, "Look at this Asian person being a hypocrite, you're all like that." Just like she suggested beeny's cooking smells like shit, but is happy to stuff her face with it, while not giving equal hospitality. (And yes, I also understand that she might not have much food in if they really don't eat much, but it's pretty piss-poor hospitality.)
I don't think "digging back" really helps, though I can fully understand why you want to, beeny. My MIL is mind-blowingly insensitive at times (hell, I probably am too but by all the small fishes, she's Olympian standard ) but over the years I have come to understand that it's not malicious in her case. With yours, I think it is.
And all I can suggest is that you try - very, very hard - to rise above it. My teenage son recently confessed to me that he doesn't want to visit his granny (my MIL) because he doesn't really like her very much. Her loss....
The reason he doesn't like her very much has to do with her mind-blowing insensitivity, and I've tried to explain that she's like "that" with everyone, so it's not personal. He's a fabulous young man and will continue to sacrifice the odd afternoon for his gran, but it'll be done out of duty, not love.
That's where your MIL will really lose out.
I'd rather my grandchildren (er, hypothetically speaking) visit because they actually want to see me.