what do you exactly mean "spammed by the appliance" ? do you mean the appliance block incoming mails from those webmail services because it considers them as spam mails? If that's what is happening please finetune the spam scores that applies.
You also state mails that are sent to those domaind are blocked as spams (?). If I understood you correctly, I'd say you do not need to enable anti-spam check in the outbound policy (except you relay emails from a third party organization to those gmail, yahoo etc. addresses).
you have a number of options to regulate checks performed on mails from gmail, yahoo, like putting the adresses on the Permit Sender list, or create a different policy in which different anti-spam scores exist (or disable the anti-spam check altogether), etc.