This is not a firewall issue. This is not a FF issue. This is a Ancestry.com issue.
Brand new iMac (Mtn Lion), no firewalls, sparking fast DSL -- I know I'm connected and I know FTM knows I'm connected because it's offered to update the software. If it has enough clearance to go out, spot the difference, report back, go back and get the new software, it bloody well should take a string of characters in plaintext.
If this is an "IE needs to be your default browser" issue, then that's moronic if they're selling a Mac-version of this software.
In the meantime, this is crippled and I shall be requesting a refund.