To understand the modern partisan divide over science, we need to go back to the origins of the Christian Fundamentalist movement in the late 19th century. There's an article on it in Brittanica that's worth reading in its entirety, but it sums up things nicely in the opening paragraph:
Christian Fundamentalism [is a] movement in American Protestantism
that arose in the late 19th century in reaction to theological
modernism, which aimed to revise traditional Christian beliefs to
accommodate new developments in the natural and social sciences,
especially the theory of biological evolution. In keeping with
traditional Christian doctrines concerning biblical interpretation,
the mission of Jesus Christ, and the role of the church in society,
fundamentalists affirmed a core of Christian beliefs that included the
historical accuracy of the Bible, the imminent and physical Second
Coming of Jesus Christ, and Christ’s Virgin Birth, Resurrection, and Atonement.
Consider the condition of the US in the late 19th century. On the Eastern seaboard there was rapid industrialization, with all the consequent social problems that entails, and a growing intellectual/academic sector that promoted a secular worldview. The deep south was still reeling in the aftermath of the Civil War, which upended the traditional social institutions. The Western territories were beginning to open up, and was still a somewhat lawless and amoral region, known (anecdotally, at least) for violence, gambling, prostitution, gold hunting, and other less-than-upright activities. Huge numbers of immigrants were entering the country to work in factories, to settle in the West, to seek out their fortunes. And of course, this was the beginning of Marxism, Darwininsm, and eventually Freudianism, the three great changes in European thought that began filtering over into the the US. It was a moment of great change and unrest, and that moment put a strain on the largely Christian population that was already established.
Christian Modernism was a movement that called for Christians to embrace these social changes (within reason). It wanted to relax and revise some of the points of Christian Liturgy that conflicted with modern social changes: embracing blacks and foreigners as brothers in Christ, accepting scientific principles that conflicted with age-old teachings, tolerating secular amorality in order to better focus on redressing immorality. But many Christians found this 'modernist' movement troubling. They thought indulging these modernist revisions would gut the church and render it powerless to fight against moral depravity, resulting in the dissolution and destruction of Christian ideals and communities. And there was plenty of anecdotal evidence to back that up, particularly in stories of young people leaving small Christian communities to seek out their fortunes in cities, or to find that mythical gold strike out in the Wild West. These Christians organized themselves as Fundamentalists, who asserted the uncompromising and absolute truth of Christian teachings, and rejected outright both the social upheavals they saw and the secular-scientific worldviews those upheavals ostensibly came from. All of this came to a head in the 1920s, when Tennessee passed the Butler act which made teaching evolution a misdemeanor crime — the setting for the famous Scopes trial — and a number of other states followed suit with similar laws.
The point is that in the 1920s Fundamentalism went from being a purely religious movement to establishing itself as a political movement. And while Fundamentalism has been highly successful as a religious cause, it has (in the years since the Civil Rights movement) suffered any number of political setbacks. Laws against teaching evolution or requiring the teaching of creationism or intelligent design have been overturned; the right to abortion has become enshrined in law; religious displays and monuments have been forced out of public spaces: step by step, the US has moved away from being a Christian nation to being a secular or faith-independent state. These political losses have chaffed at the Christian Fundamentalist community.
Now, somewhere around the Reagan years (the 1980s), the GOP began constructing a new coalition among various groups that felt disenfranchised by the Liberal swing of the Federal arena. They brought together deep South segregationists, small town ('family values') conservatives, Right-libertarians and hard-line capitalists, neo-McCarthyists, and yes, Fundamentalist Christians, many of whom had little in common with each other except:
- They opposed the inclusive communitarianism of the left (for widely divergent reasons), and
- They opposed the entry of science into social and political affairs
The second point is derived from the first. Since the 1960s, the Left has bolstered its moral worldview with scientific research, using such research (variously) to show the damaging effects of pollution; describe social stratification, systematic racism, or the oppression of women; undercut religious teachings and attack religious viewpoints; etc. Conservative groups don't dislike 'science' per se. They dislike science when it is used as part of a social/moral argument. Part of that, of course, is the fault of those who use science poorly and aggressively — certain anti-theists, certain progressive 'warriors,' etc; those who try to leverage science as a hammer to destroy social institutions they dislike — but part of it is the fact that scientific arguments, done well, are extremely difficult to contest, and that creates a moral dilemma. For instance, it would be perfectly feasible for someone to look at climate science and make a moral argument like: "I accept climate science, and accept the idea that humanity is altering the world's climate, but I reject the conclusion that this is a moral wrong, and see no reason to change anything." But making such a moral argument often sounds heartless and cold; it is socially and psychologically easier to discredit or obfuscate the science itself.
So in short, the reason why there is such a strong partisan divide on the credibility of science is that the GOP has explicitly constructed a coalition that opposes the Federal trend towards liberalization, and rejects the mass of scientific research that trend relies on.