Sure, ideology impacts formal reasoning, but if you look at the examples given the participants have good reason to reject the conclusions of formal logic that is based on terrible premises.

Despite the result of a simple sequence of sentences divorced from reality, cigarettes really are bad for you and salads are good (depending on their contents).

In study 1) participants might disagree with dangerous drugs being banned, and they disagree that marijuana is dangerous. In 2) premise 1 seems relatively straightforward, then premise 2 is a highly ideological belief (as is the point of the study).

I don't think this is very revealing. When you add 1+2 and get 68445788, you are suprised by the conclusion and check your work. People responding to this aren't dumb, they just aren't playing along with what they regard as faulty reasoning. Basically, they are likely saying I know what the researcher wants me to say, but this is wrong and I won't go along with it.