After I log in, I get a security warning that tells me that I am about be redirected to a connection that is not secure. Is it safe to continue?

Yes. The remote access system is set up to use Secure Socket Layer (SSL) technology to encrypt your barcode and PIN. After you have successfully logged in, you are connected to a database. The browser is just letting you know that you are moving from a secure site, to one that does not need this type of security.