Republicans have the most in common with which minor party?

Delta Sigma Phi initiation party

Hmmm. Maybe you mean Tea Party...

The question is probably referring to one of the major parties listed here.

http://en.wikipedia.org/wiki/List_of_political_parties_in_the_United_States

Which one of these works the best?

Constitution Party
Green Party
Libertarian Party
Modern Whig party
Reform Party
Socialist Party

http://www.modernwhig.org/handbook/who-are-modern-whigs/what-we-believe

I suspect Republicans like to think they share these principles.

However in real life they seem to be closer to:

http://www.constitutionparty.com/our-principles/key-issues/

To identify the minor party that Republicans have the most in common with, we can look at their shared ideologies, policies, or principles. The Republican Party is often associated with conservative values, limited government intervention, free-market capitalism, and a focus on individual liberties and personal responsibility.

Based on these factors, the minor party that Republicans tend to align with most closely is usually the Libertarian Party. Libertarians also advocate for limited government intervention, fiscal conservatism, and individual freedom. They typically support free-market capitalism, deregulation, and reducing the size and scope of government.

It is important to note that political ideologies and party platforms can vary over time and across individuals, and there may be differences in specific policy positions between the Republican Party and the Libertarian Party. Additionally, minor parties can have varying levels of influence and representation in different regions and elections. Therefore, it is always advisable to research and compare specific party platforms and positions to gauge the degree of alignment.