What cement board can I use for an outdoor bbq?
Edited to remove ANY subjectivity:

HardieBacker is made from wood (cellulose fibers) and cement and carries a limited warranty for exterior use and only in certain climate zones. See HardieBacker's 10-Year Limited Warranty for Exterior Use

Durock is made from cement and fiberglass mesh. Wonderboard and others are made similar to Durock.

Subjectivity Here:

Obviously, there is a reason for the substantial difference in warranty between interior and exterior applications. My belief is that the cellulose will eventually break down from the shifting between warm humidity/ and freezing temperatures, especially in applications that would limit the ability for the product to appropriately air out. Durock is cement and fiberglass, and while both products will react to hot/cold like poured concrete, I would prefer the product that does not use wood. Given that they cost about the same, I would rather use something that the manufacturer expects to be able to withstand the 10-year warranty, over one that doesn't expect it to in nearly half the U.S.

But again, that is my subjective opinion.