Some basic principles must be in play before a society can be defined as free. One of those is that every person is treated equally under the law. No one should be above the law, and no citizen or group of citizens should be singled out from being protected by that law.
Equality is not an easy principle and was one of the root causes of the Civil War when the first Republican president, Abraham Lincoln, emancipated the slaves. So when Liberty Republicans hear “How can you call yourself a Republican and support gay marriage?!” that is doubly puzzling. The correct response should be “How can you stand against equal application of law and call yourself a Republican?”
The Fourteenth Amendment of the Constitution makes it clear that if there is a law, it must apply equally to all American citizens. The Liberty view of marriage, then, is either stop having the government license marriage, allowing each religion to define it as they see fit (meeting all other laws that apply as to age of consent), or apply marriage laws equally to all adult citizens regardless of factors like gender.
Liberty Republicans generally believe each religion should be free---as assured by the First Amendment---to marry or not marry a couple, regardless of race or gender.
Now, since very few discussions of gay marriage or freedom of religion can take place without talking about it, Liberty Republicans oppose non-discrimination laws that prevent people from practicing their religion and following their conscience freely. In that, we frequently run afoul of people who ask us if that stance would have allowed continued discrimination of races during the Civil Rights era. (Note, Civil Rights laws were another Republican-led crusade.)
There I would point out that cities, school districts, and states had laws that segregated people by race. There's a difference between a public institution practicing discriminatory policies in our names, and an individual or private business doing so with their own property. If Joe Smith wants to have a private lunch room that does not serve blacks, or women, or gays – if Joe Smith did not receive any state or government funding – then he should be allowed to have his bigoted lunchroom.
I just hope he would post his policy in his store front window, so I could be sure not to spend my money there.