I have no problem using public wifi but I make it a point to never type in any passwords for anything such as online banking, though it could be worth asking them at the air port and checking what kind of security they would use.
Not only wouldn't I do any financial transaction on public wifi, I wouldn't do anything that requires account ini unless I'd set up an account not linked to anything else that I might care about. I wouldn't use Facebook on public networks, for instance, because I don't want to risk someone hijacking my contacts and spamming them. It can be a mess to clean up, even if it doesn't cost financially, and your info is exposed.