I agree that this is possible in principle, but from what I observe in practice, libertarian arguments have extremely low weight in such trade-offs, except for the tiny minority of principled libertarians, who form a small and reasonably well-delineated cluster. When it comes to issues that are otherwise neutral and uncontroversial, people will normally default to the libertarian position. However, as soon as an issue has any bearing on ideology, tradition, religion, ethnic identity, political power, economic interests, status hierarchy, etc., etc., people normally assign near-zero weight to libertarian arguments, except insofar as they provide useful material for unprincipled rhetorical ploys.

This seems exaggerated to me (although I agree that the tendencies you mention exist and are significant). Consider, for example, the famous incident in which the American Civil Liberties Union defended a Nazi group's right to demonstrate. The ACLU was and is a non-fringe organization, and likewise, the position that "Nazism is despicable, but freedom of speech and assembly is more important than silencing Nazis" is reasonably mainstream in the United States. Similarly, the idea that "Drug use is bad, but marijuana should be legal" seems not-uncontroversial but also non-fringey.