Books

A libertarian who decides they want no government control is an anarchist.

If they want limited government control they are libertarians.

They are similar but differ on a key issue, government control. And that's the biggest issue for anarchists.

If I say I am an anarchist it means I do not want the government in public libraries at all.

Now if you need to rip the bandage off fast or slow is debatable, but there is no debate on if the bandage needs to come off completely for an anarchist.

If I say I am a libertarian it means I want the government limited in public libraries.

Again, how fast it needs to change is debatable.

They both rely on the goodness of the people rather than a government. They both share pretty much the exact same ideology, other that anarchists are for "No Authority" and libertarians are for "Limited Government"

Personally, I don't think a public library would exist in today's world without the government.

You want me to donate money so people who cannot afford books can go and check out physical copies of books they can look at digitally for free?

I'm better off donating to a homeless shelter or another cause.

Libraries are only good for homeless and poor now because we currently do not give them better options.