From what I can gather on white dwarf variability, this applies mainly to very young white dwarfs (which would be still extremely hot), or white dwarfs that are accreting material.
The former scenario shouldn't be an issue since we're looking at older white dwarfs -- ones that have had enough time for a planet to form or migrate to the new habitable zone and evolve life on them.
The latter scenario would imply a semi-detached stellar companion, ie one that is orbiting close enough such that its outer atmosphere is being pulled off the star and accreting onto the white dwarf. But having a stellar companion orbiting this close would pretty much guarantee no habitable zone around the dwarf to begin with, so there's no sense looking for such habitable planets in this type of system.
What we're left to look for are old, dim, solitary white dwarfs whose surfaces have cooled to perhaps <10000 Kelvin, probably more like 5000 or 6000 so that there isn't as much UV radiation. (White dwarfs emit essentially as blackbodies, so a hotter surface implies more shortwave emission like UV and Xray). You could also possibly have a white dwarf and a more distant companion, but you'd need to consider how much light is the planet getting from the companion in addition to the dwarf.