It seems true that the Republican Party is more socially conservative in recent years. Republicans ramped up already strong opposition to abortion and embryonic stem cell research, euthanasia, expansion of civil marriage and adoption to same-sex couples, non-marital sex, and the privatization of religious belief. At the same time, many Republicans have become even more supportive of traditional family values, the prohibition of drugs, and the censorship of what they consider to be obscene.
The 2010 midterm elections saw Republicans regain control of the U.S. House of Representatives and many of those elected associate themselves with the "Tea Party" — a grassroots faction of conservatives that formed to protest high taxes but quickly embraced socially conservative ideals.
Some younger Republicans, however, are shifting at least some of their views on social issues. While President George W. Bush and presidential candidate John McCain both campaigned in strict opposition to same-sex marriage, their daughters Barbara Bush and Meghan McCain have gone on record supporting marriage equality for gays and lesbians.
Some Republicans, such as current Minority Whip Eric Cantor, claim the root of Republicanism is the belief in free markets and in individual responsibility; therefore, he would embrace even Republicans who support abortion rights. And often, Republicans from major urban areas, such as New York City's mayor Michael Bloomberg and former California governor Arnold Schwarzenegger, are far less concerned with social issues than fiscal issues.
Perhaps more socially liberal Republicans will eventually become the Party mainstay, or maybe conservatives will dig in their heels and keep control. This is a battle that's seemingly ramping up among the Party as a whole.
And for the record, Democrats have their own discord on social issues. Southern and rural Democrats are often elected on labor issues rather than social liberalism. These Democrats are far more likely to support abortion restrictions and traditional marriage, so the battle over social issues is not just a Republican one.