It is impossible to answer this question for every Republican; each may have their own reasons for the determination they've come to. So, the following answer is a representation of the reasoning, in the circles I travel, that the prospect of man-made climate change is questionable. There are four main points, highlighted below with amplifying information. They will be followed by a summary.

History of Data Manipulation
There are two significant incidents where it has been revealed after the fact that those developing the man made climate change narrative have made demonstrated lapses in integrity. First was the Hockey Stick graph, first released in 1999 (Mann, Bradley, and Hughes). It was subsequently weighed down with challenges to the statistical methods it used and a critique questioning the choice to minimize the statistical influence of the Medieval Warming Period, the latter highlighted by the differences in the IPCC reports between 1990 and 2001. The integrity of the work was further tainted by the hacking of climate research email servers which provided a perspective of conspiracy (more later). More recently, the choice of NOAA to 'adjust' recorded temperature information, lowering earlier records and raising current records, furthers the perspective of manipulation.

Data Not Available for Review
In addition to the question of data integrity, there is an ongoing complaint that many of the reports and news articles present the results of an review, without providing the source information and methodology for evaluation. With a Bachelors in Mathematics and a Masters in Systems Engineering, not having access to the raw data increases the skeptical approach.

Active Conspiracies
While some level of confidentiality and opaqueness is expected in scientific exploration, the lengths that the proponents for climate change goes to doesn't help the perception that something untoward is going on behind the scenes. This is worsened be previously referenced release of emails from within a climate change organization that reflected those concerns.

Abandonment of the Scientific Process
The line that creates the most cringing response is "the science is settled," with the impression being that it has been proven that man made actions have an influence on climate change. That isn't how science works. It far easier to prove the negative, that a thing doesn't exist, than to ever prove a thing does exist. Consider the level of proof required for even the simplest of scientific claims. In this case, the intention that the exhausts of man made technologies has an influence on climate change (again, more later), requires an in depth understanding of a multitude of factors, which non-exhaustively includes: solar cycles, irregularities of the planets orbit, irregularities of the planets rotation, the cyclical nature of prevailing winds, interaction of the moon on the tides and the resulting effects, irregularities of the planet's core hydraulic rotation, shifting of the continental shelves, variation of volcanic heating influences on the oceans, and many, many more. Further, the claim that carbon dioxide is a pollutant, which is held true in order to curtail it's production, is questionable. An increased availability of carbon dioxide would encourage an expanse in plant growth.

Summary
Climate Change does exist; there are cyclical pattern that can be demonstrated in what weather does. That said, I can't give much credence to the claims that man kind is at direct fault for it.

It is impossible to answer this question for every Republican; each may have their own reasons for the determination they've come to. So, the following answer is a representation of the reasoning, in the circles I travel, that the prospect of man-made climate change is questionable. There are four main points, highlighted below with amplifying information. They will be followed by a summary.

History of Data Manipulation
There are two significant incidents where it has been revealed after the fact that those developing the man made climate change narrative have made demonstrated lapses in integrity. First was the Hockey Stick graph, first released in 1999 (Mann, Bradley, and Hughes). It was subsequently weighed down with challenges to the statistical methods it used and a critique questioning the choice to minimize the statistical influence of the Medieval Warming Period, the latter highlighted by the differences in the IPCC reports between 1990 and 2001. The integrity of the work was further tainted by the hacking of climate research email servers which provided a perspective of conspiracy (more later). More recently, the choice of NOAA to 'adjust' recorded temperature information, lowering earlier records and raising current records, furthers the perspective of manipulation.

Data Not Available for Review
In addition to the question of data integrity, there is an ongoing complaint that many of the reports and news articles present the results of an review, without providing the source information and methodology for evaluation. With a Bachelors in Mathematics and a Masters in Systems Engineering, not having access to the raw data increases the skeptical approach.

Active Conspiracies
While some level of confidentiality and opaqueness is expected in scientific exploration, the lengths that the proponents for climate change goes to doesn't help the perception that something untoward is going on behind the scenes. This is worsened be previously referenced release of emails from within a climate change organization that reflected those concerns.

Abandonment of the Scientific Process
The line that creates the most cringing response is "the science is settled," with the impression being that it has been proven that man made actions have an influence on climate change. That isn't how science works. It far easier to prove the negative, that a thing doesn't exist, than to ever prove a thing does exist. Consider the level of proof required for even the simplest of scientific claims. In this case, the intention that the exhausts of man made technologies has an influence on climate change (again, more later), requires an in depth understanding of a multitude of factors, which non-exhaustively includes: solar cycles, irregularities of the planets orbit, irregularities of the planets rotation, the cyclical nature of prevailing winds, interaction of the moon on the tides and the resulting effects, irregularities of the planet's core hydraulic rotation, shifting of the continental shelves, variation of volcanic heating influences on the oceans, and many, many more. Further, the claim that carbon dioxide is a pollutant, which is held true in order to curtail it's production, is questionable. An increased availability of carbon dioxide would encourage an expanse in plant growth.

Summary
Climate Change does exist; there are cyclical pattern that can be demonstrated in what weather does. That said, I can't give much credence to the claims that man kind is at direct fault for it.