I don't think you want to replace Android wholesale with a traditional Linux kernel, etc. That's probably far more work than you might imagine.
On the other hand, you might be interested to know there are many
folks that have managed to install Ubuntu/Debian inside
an Android device. As far as I understand it, it's not a "dual boot" setup, but more like (very loose analogy here) a virtual machine running inside Android.
There are how-tos sprinkled across the web if you search for "run linux under android"
Indeed, I even found an app
on the market (requires root as most, if not all these approaches likely require):
By all representations, these should be full-fledged linux installs which should allow access to repositories, and therefore, XBMC through said repositories.
All that said, I am not going to speculate as to performance. Though, to be honest, I think you're overly optimistic if you're hoping for any $50 device capable of streaming full 1080p video. I bought an Acer Iconia tablet for $400+ which was advertised as including the ability to play 1080p content. Playing the content on the device was choppy (and that's being generous) at release. Only after an OTA update or two did it get to the point that 1080p video playback on the device itself
was acceptable. And again, that was with arguably top-of-the-line specs when released. I can't see a $50 tablet having the horsepower to push 1080p locally much less via a wireless network connection... and then through a virtual Linux environment
But here's hoping you make an unjustifiable cynic out of me