There are two quite distinct contributors to the "disagreements over status of scientific evidence"1 to which the scientific community must be careful to respond differentially.
One is the effect of ideological frameworks derived from religious belief, exemplified in the United States by those that wish to prevent the teaching of Darwinian theories of evolution, or at least require also teaching the so-called intelligent design theory. Other examples might be drawn from other cultures, such as, fundamentalist Islam, and include social impacts such as the debate over stem cell research. In these frameworks Truth derives from a Higher Authority than the limited vision of human scientific rationality.
The other contributor is the general cultural awareness of the "sociology of knowledge" paradigm that has evolved in the past 30 or 40 years. This framework understands science as a social endeavor, governed, or at least shaped, by social status considerations, money, and...
One reason for societal ambivalence1 is the nature of modern science. All too often we hear extra-scientific statements and positions by scientists. Terms such as "the self-correcting nature of science" are used as a thin cover for reversals of statements that were made as authoritative, definitive ... in short, as scientific facts. "Science" has become bloated with whole fields based largely on assumptions, speculations, and gathering supporting (or at least "consilient" data), and calling that good enough. It's no wonder people are no longer impressed by science when confronted by further pontifications that aren't backed by repeated observations and experimentation.