The Advocates for Self-Government use the World's Smallest Political Quiz to try to find persons who do not self-identify as libertarians, but who react to libertarian ideas without hostility. Their idea is, if you want to persuade people, start with those who are already fairly open to the idea. Save the hard cases for later.
This also offers us the opportunity to target outreach. Don't try to convince a serious liberal or conservative to adopt a libertarian view, but rather seek alliances on issues that have space for common cause.