My response to it is that that there is a difference between an odd intellectual position, theory, or philosophy, and populist anti-intellectualism that rejects all science and philosophy altogether for popular beliefs and 'stock-knowledge" taken for granted in particular social groups. The creationism debacle in the US seems to be a case of the latter - a rejection of anything "cultural" and "intellectual" in favor of simple folk beliefs. This seems to be a genuinely home-grown American populist phenomenon, albeit politicos manipulate it mercilessly to their advantage.
As far as to what to do with it, at this point in my life I came to the conclusion that it is not possible to save people against their own will. If someone desperately wants to delude himself with myths, lies, self-deceptions, illusions of status, scapegoating, or indulgences - let him, even if in the end these delusions will hurt him. People love their delusions and as long as it is so, there is nothing that others can do about it.
The most reasonable way of dealing with this problem is trying to insulate oneself from the possible harmful effects of such people - letting them alone and not letting them interfere with other people's lives as much as possible. Effective fighting them is incompatible with the norms of democracy, rule of law and civilization, while mere engaging them in debates is completely useless and may have the dangerous effect of giving them legitimacy.
However, if they indeed become a threat to public institutions and order in this country - which is a real possibility, but not very likely one - then the only two choices is to "fight them by any means necessary" i.e. by force rather than persuasion, or leave the country altogether. My only hope is that anti-intellectualism and ignorance almost never paid off in the long run - the spoils went always to those with more knowledge, better science and better technology.
On that note, have a happy dead-bird-eating day.
Wojtek