Explaining the intellectual position without saying that I accept it (my actual views on this are "it's complicated"):

Arguments against KYC usually go hand-in-hand with the belief that AML statutes are a constitutional overreach and grant the federal government powers that they should not have. The logic is that the government's only role is to provide a stable currency and enforce contracts, and that anything else is involving the government in business that it has no business being in. What's done between two consenting parties should remain between two consenting parties.

Note that such a position usually doesn't have a problem with banks having information on their customers, for the purpose of judging credit risks. But it holds that such information should only be used for judging credit risks, ie if you are just depositing and withdrawing money that has already been earned, the bank should be agnostic to this. And they also object to this information being shared with a central clearinghouse where it can be used to cut off all access to the banking system rather than just one specific bank who objects to the source of funds.