Why does Costco refuse credit card payments from non-Costco members in the United States?

Potentially because credit card payments cost them money, and if you are a member, you basically pay those back through your annual fee. For non-members, there is not enough margin left to cover those additional cost.

I suspect it's to discourage excessive use of somebody else's account as a guest. They want to sell more memberships instead of having one person let many people into the warehouse.

I lived in a college town with a Costco and they had a policy there that they'd take one payment and receipt per cart or member. Therefore, roommates or friends using guest privileges, which was very common, would have to reconcile the purchases and payment later.

Outside this college town, I haven't noticed them enforcing this policy, like when I ask them for a separate receipt for business purchases.

Amazon Prime did something similar when they changed the Prime guest policy to require sharing the same address and payment methods.

Costco's whole business model relies on membership. Costco wants you to be a member so Costco makes things difficult for non-members.

I believe Costco only accepts Visa cards. They offer a Visa card with enhanced membership, and I strongly suspect that part of the deal, for bringing many thousands of new accounts to Visa, is that the usual merchant fees for people who use that card are greatly reduced or waived for Costco purchases.