While I understand your desire for the crispness/pop of the white fabric, my experience with the muted dyes of batiks is that I would go for the beige instead. I just haven't been happy using white with batiks, typically I use for black as my neutral when working with them (and often when working with solid colors as well). Keep in mind that the way a log cabin is made the darker fabrics will reinforce the medium/lighter ones as appearing darker, especially when using a consistent fabric on the light side.
Don't know if I can express this well -- but will you do be doing both right angles for each row out of the same fabric or will it be entirely scrappy? Either way it works.
The good news is with batiks it will be lovely no matter what you decide!