I'm not sure what would fit into this criteria mind, a few examples may help me respond (as I'm unsure what a government my try to legislate in, in which evidence can't be obtained) .
Education is a good area for a start. Several of the primary education theorists are completely at odds with each other, most are also not really backed up with any solid scientific research either (the problem of ethics rears its head here quite a bit.
Evidence based decision making also tends to ignore the emotional impact or can be at a macro level and ignoring the micro level. Immigration would be a prime example of this, on a macro level the economic benefits are reasonably clear, however this completely ignores the micro level and the impact on certain socio economic groups. It also dismisses the emotional impact of mass immigration as "xenophobic" or "racist".