Hi its definitely not the new chip in your MacBook Air. One other person has also reported this happening on iOS as well. So it could be a issue with Costco's site. I'm glad you can still login using your old MacBook & iPhone.

I think this issue is gonna take a while to investigate since not everyone has a Costco account. I will see if this issue has a bug report filed as it sounds like people with newer Mac devices might not be able to login to Costco.