An anti-conservative is someone who wants to take a position simply because it is oppose the conservative position is, without any rational basis.
Sometimes the logic is simply a matter of disliking someone or an institution perceived to be conservative and then adopting views that are the opposite of other disliked person. For example, "the ______ church holds this position, so I'm against it!" Or, to take another example, "my [father/mother/ex-husband/ex-wife] thinks such-and-such, so I'm against that!"
Note that there is not logical basis for the anti-conservative approach. Anti-conservatives do not seek the truth or arrive at positions based on a logical, defensible process, but merely gainsay what is said by conservatives.
It is widely recognized that phonics is a superior way for children to learn how to read. Yet there are political and financial motivations for some to oppose teaching phonics, and instead use less effective approaches like "look-say". More money can be made in selling textbooks to those who take longer to learn how to read, or do not learn to read as effectively. Moreover, one political party can benefit relative to another by having a higher illiteracy rate. So there are incentives to oppose phonics.
Those against phonics lack logical arguments that would persuade an objective observer, so they resort to appeal to the anti-conservatives: One widely used book claims that phonics is nothing short of a far right plot "to promote a religious agenda" and inculcate "docility and obedience on the part of the lower classes."
Other examples abound. "In many [British] teachers minds, phonics equals right-wing, traditional, drill and skill, boring, anti-child-centred Gradgrind education. Over in the United States, phonics is portrayed as being closely aligned to the Christian fundamentalist right. The No child left behind act mandated phonics. Hell, Dubya loves phonics, so it follows that all right-minded progressive folks need to be against them."
- Reading Process and Practice, From Socio-Psycholinguistics to Whole Language by Constance Weaver.