So it’s profile specific. Could even be browser specific. Something is not right with the communication path. For example, you create a hosts file entry and you point it to your dev server which does -not- have the name https://www.yourdomain.com << that would give you a cert error.
When you use nslookup, you’re querying against your nameserver. Do you get the same ip when you ping from a command line?
Of course, that’s all machine specific and it wouldn’t matter who was logged in.
Also, when you’re getting the cert error, view the cert. Does it match correctly?