Final answer:
The Republican Party has made significant gains among white fundamentalist Christians in recent decades, mainly due to their positions against abortion and the support of school prayer. The alignment of the Republican Party with the interests of evangelical voters was solidified during Ronald Reagan's campaign and presidency, leading to a political realignment, particularly among Southern voters.
Step-by-step explanation:
The party that has made big gains in recent decades among white fundamentalist Christians is the Republican Party. This shift can largely be attributed to the party's stance on issues that resonate with evangelical voters, such as opposition to abortion and advocacy for school prayer. As a result of the Republican Party's positions on these social issues, they have become a crucial constituency within the party. Ronald Reagan's campaign and presidency played a significant role in cementing this relationship in the 1980s.
Conservative Christians have been drawn to the Republican Party's commitment to what they perceive as traditional family values, a small government that gives more regional autonomy, and a conservative approach to social policies. As the Republican Party integrated these concerns into its platform, they attracted a considerable following from the religious right, causing a marked realignment in American political allegiances, particularly in the South.
However, it is also important to note that while the Republican Party has focused on these social issues, there have been instances where social conservatives have felt that their expectations were not fully met, with Republican leaders sometimes placing greater emphasis on fiscal conservatism once in office.