Libertarians adhere to the political philosophy that individual rights must be acknowledged and protected by the state. Thus, libertarians support a free market economic system absent of government interference, rejecting state socialism and corporatism, otherwise known as "crony capitalism."
Acknowledging the rights of all individuals regardless of class, race, sex, gender, creed, etc., libertarians believe in the free exchange of goods and services and that all people may own property and be free to compete in the marketplace.
Capitalism is typically defined as a political and economic system controlled by a network of freely operating private businesses and owners. By this definition, libertarians are capitalists because they believe in private ownership and individual rights.
Corporatism, on the other hand, is when the state is controlled by corporations, allowing big businesses to compromise or erode individual liberty with impunity, favoring executive shareholders and large interest groups.
Socialism is the economic theory where the means of production would be collectively owned and wealth distribution would be regulated by the community as a whole, which tends to mean state-controlled. State socialism has the propensity to lead to authoritarianism.
Libertarianism rejects any economic practice that facilitates the enmeshment of business with the government--be it corporatism or socialism--that infringes upon the freedoms and rights of individuals.
Answering the question 'Are libertarians capitalists?' relies on how the word is defined. Many political and economic papers published since the 18th century have different perceptions and definitions of capitalism, examining what it truly is in theory and practice.
The debate will likely be ongoing.
The key idea to remember, whether a libertarian describes themselves as a capitalist or a libertarian socialist, is that libertarianism advocates for free markets and the preservation of individual liberty.
In a free market, individuals can structure companies however they choose.
If a company is structured to have one owner and many employees, and workers have given their consent to the dynamic, then libertarians support the freedom for this business to operate.
If workers choose to organize a company with equally shared ownership of the means of production--known as libertarian socialism, worker-owned businesses or collectives--then libertarians support the freedom for this business to operate.
While many libertarians proudly call themselves capitalists, many choose not to, insisting that their political and philosophical devotion to libertarianism alone defines their economic stance.
For more information, see 'What is Libertarianism?'