I just put in a wood burning stove and hearth last year and I used the backerboard for the floor as a fire stop per code and that stuff stunk.
I would guess there must be some chemicals in it that make it smell like that since I have done cement work and never smelled a smell like the backer board.

You're better off with a plastic liner on the walls, leaving the bottom open for drainage. Backer board is expensive, brittle, and is not waterproof - won't add anything but weight to your raised bed walls. It's only used on floors b/c it's cheaper and easier than a mud bed for tile. You have to (or should, if you want it to last)install a waterproof membrane to use it in showers since grout is porous and will let water/water vapor through to the backer board, which will eventually fall apart (though perhaps it might last longer than the 2x4's!).

Exterior Hardiplank would probably work better, but it would need support.

There is "hardiboard" tile-backer, and then there is "dura-rock", which IME is quite durable outdoors. I've had some outside for years. I don't know what chemicals are in it.