That said, why is the emphasis on constitution (BTW, do you mean any constitution or US constitution in particular)? Constitution is just a special kind of law after all and I can totally imagine libertarians claiming that it is inadequate, pushing to change it and make it more aligned with their principles.
In the USA we have the Bill of Rights that protects each person from government overreach, such as the 1st amendment which protects freedom of speech, and the 5th amendment against testifying against yourself.
The government however often passes laws that violate these rights, and then the courts have to overturn laws that are unconstitutional because they violate our rights.
I am of the opinion that the government is a very dangerous entity with unlimited power and ability to harm citizens, so we should always be skeptical of all laws passed and work as much as possible to limit the power of government.
Libertarians aren’t anti-law, they are pro-constitution. Libertarians are against the drug war, pro-marijuana legalization, against civil asset forfeiture, and trying to end the endless wars waged in the Middle East.
You will not find a better friend than a libertarian if you ever find yourself arrested or sued for any reason. Judges inventing laws is the antithesis of the belief system - libertarians follow the law as written.