Copyright enforcement is not a form of censorship.
Copying someone else's work and presenting it as your own is not protected speech, it is fraud. If you want to still consider this speech, someone is using it to actively and intentionally harm others.
If you're so intent on free speech, how would you feel if someone followed you around screaming profanities and abuse? Are you engaging in harmful and immoral censorship by calling the cops to remove this person? Are you suppressing his right to free speech by taking out a restraining order?
This doesn't even take into account the endless lobbying by Disney to pervert copyright law into what it is today.