(your browser will likely alert you to them being invalid, but how often have you clicked such warnings away in the past? Lots of websites used to have such warnings for using self-signed certificates not issued by an "authority")
The certificate could also be issued by an authority that your browser doesn't have in it's collection of certificate signing authorities; however, banks don't use fringe signing authorities. Learn that whenever you click away such warnings, you can't be sure the connection is secure - do not use such sites for sensitive information.
I don't worry about using any of
my devices to do online banking over any network (school, public library, neighbor's open wifi, etc.). Certainly someone could attempt a man-in-the-middle attack on a public network, but your browser should detect and warn you because they won't have a proper certificate saying that they are your bank's secure website. They might catch dumb people who ignore the security warning (or have turned them off), but once you're communicating over SSL with the owner of the site's certificate, your risks are pretty low (at least the weakest link in security is probably now your device, not the network connection).
I'd be much more inclined to take advice to avoid public networks for online banking if they first advised you to not use your regular user account for online banking. Create a user profile on your device that you only use for online banking. Every app that runs in your user account is potential spyware - this is orders of magnitude more likely to be a threat than someone establishing a man-in-the-middle attack with a spoofed certificate that your don't get warned about (still pretty small if you don't download software from shady sources). Sure, if you're going through the trouble to log out of your regular user account and into your financials only account because you're worried about security, go ahead and also avoid using public wifi for the internet connection.
