Welcome to Fr.
If you notice, Reagan wasn’t a libertarian, and all that you have from him is that little quote from 1975 when during his campaign, he was being interviewed by the libertarians, solely for a libertarian audience, that quote looks pretty lonely when explained.
Reagan was a conservative and did not endorse the leftism of the libertarians, although they largely supported his conservative economics.
Here is the leftists agenda hidden behind the Libertarian Party curtain.
Libertarian Party Platform:
Throw open the borders completely; only a rare individual (terrorist, disease carrier etc.) can be kept from freedom of movement through “political boundaries”.
Homosexuals; total freedom in the military, gay marriage, adoption, child custody and everything else.
Abortion; zero restrictions or impediments.
Pornography; no restraint, no restrictions.
Drugs; Meth, Heroin, Crack, and anything new that science can come up with, zero restrictions.
Advertising those drugs, prostitution, and pornography; zero restrictions.
Military Strength; minimal capabilities.
These should be restricted to the same degree as the addictive mind-altering legal drug alcohol: sale only with a license, no sale to minors, etc. The War On Drugs is failing in all the ways that alcohol Prohibition failed.
(And as far as "anything new that science can come up with": they come up with new drugs because those new drugs are legal until law catches up; there will be fewer if any new drugs if they no longer enjoy that legal advantage.)