Matt Grossmann and I have a research project (book manuscript in progress!) in which we argue that the Democrats and Republicans are fundamentally different kinds of parties. We view the Republican Party as the vehicle of an ideological movement—the conservative movement—while the Democratic Party is instead a coalition of discrete social groups, in which ideology plays a role but is not the party's defining purpose.
One of the many manifestations of this asymmetry is the shared assumption by virtually all of the Republican Party's leaders—including both elected officials and unelected activists, interest groups, and media figures—that the party exists to advance conservative principles. If a policy position, initiative, or political candidate is conservative, Republicans should properly be for it/him/her; if it/he/she is not conservative, all Republicans in good standing should rise in opposition. Republicans may sometimes disagree among themselves about which policies are conservative, or about which strategies and tactics are most appropriate for furthering conservative principles in a given situation, but the party has reached a virtual consensus that the advancement of conservatism is its fundamental reason for being.
This attribute of Republican politics has allowed the conservative movement to achieve a great deal of political success over the past 50 years of American history. But there are drawbacks. Venerating conservative principles can make it difficult to define limits to any rightward push within the party. The most popular play in the Republican primary playbook is always to label your opponent as insufficiently conservative, which creates an incentive for politicians worried about being attacked from their right flank to maneuver themselves further and further towards the conservative pole—or risk losing to more extreme opponents who may be vulnerable to defeat in general elections, like failed Republican Senate candidates Christine O'Donnell, Sharron Angle, and Richard Mourdock.
For those Republicans who view the rise of Donald Trump with alarm or outright panic—whether because they disagree with his views, because they believe him to be an unqualified and potentially dangerous president, or because they worry that his nomination will prove disastrous for the party—one of the biggest challenges so far in the campaign has been the identification of a line of attack that effectively punctures Trump's popular appeal within the mass base of the GOP. Instinctively, many Trump critics within the conservative movement have attempted to claim that Trump is not a true conservative—and is therefore by definition undeserving of Republican support. The advantage of this line of argument is not only that it might prove effective in dissuading Republican voters from backing Trump, but also that, whether ultimately convincing or not, it preserves the critic's position as a conservative in good standing, while a "Trump's too far to the right" message renders the speaker vulnerable to the charge that he or she is merely a squishy moderate.
Today, House speaker Paul Ryan was asked about Trump's proposal to ban Muslims from travel to the United States. Ryan surely views Trump as a horror show for the GOP. Tellingly, however, he chose to characterize Trump's plan not just as extreme or un-American but also as "not conservatism." This argument has not yet succeeded in persuading Trump's supporters, but in Republican circles, it's the most damning attack one can make on a policy—or a candidate.