The LP at most state and local levels is cooperative, and one of our former RLC Board members is now an LP state chair. An RLC member who is a former LP state chair and U.S. Senate candidate has recently signed up as a surrogate speaker for an incumbent U.S. senator for his re-election effort. So it can go both ways. In California, we endorsed LPer Dick Rider's non-partisan bid for San Diego County treasurer. We would lose our credibility if we endorsed LP candidates against Republicans, as the GOP is both very mindful of this and is somewhat suspicious of libertarian Republicans anyway.
Individual members can and do support whomever they wish.
We appeal to constitutionalist, limited-government types of all kinds, including many who may describe themselves as principled conservatives. However, the RLC is open about calling ourselves the organized wing of the libertarian Republican movement. We are about making libertarianism an asset, not a liability, in politics. My personal view is that the LP is no longer a real political party. It is a political education vehicle with the form of a political party but one in which its primary purpose is to build the organization rather than to elect libertarians to public office.