Social conservatives are the conservative movement, the anti social conservative and open border libertarians only have 226,000 registered members making it irrelevant in almost all cases. It appears to be only the sixth largest party of 51 national parties.
This is from the 2004 Libertarian Party Platform.
Immigration:
“We call for the elimination of all restrictions on immigration, the abolition of the Immigration and Naturalization Service and the Border Patrol, and a declaration of full amnesty for all people who have entered the country illegally.”
Don’t forget the Libertarian platform in 2004 also called for a withdrawal from Iraq. And they nominated Mr. ACLU Bob Barr.