Christianity is heading for a full allegorization

[Angrboda]

Since we all have characteristic ways of thinking, and these ways of thinking are always derived from our culture, I don't see how we can be said NOT to have an ideology. 

Especially if we have strong beliefs about how the world could be better, then that's our ideology.

Nope. Ideology is a set of beliefs that must not be questioned but obeyed no matter what the evidence shows.

No, that would be dogma. We already have a word for that. Ideological in the sense of being pejorative typically means that one's ideology dictates their beliefs to a greater extent than is common in the average person, or is held irrationally. Much like racism, it is a matter of degree. Having implicit biases against a specific race makes you racist according to a strict interpretation, but the pejorative use of the term is reserved for those in whom biases against a specific race are more significant and consciously held. Strictly speaking, everybody has an ideology, except for the fact that the word is not often used in that sense in colloquial discourse.