Firefox already has SEED for TLS in the crypto library we use (NSS). AFAICT, the problem now is mostly getting bank websites to change. I believe some Korean banks have indicated that they will start supporting the standard mechanism in addition to the ActiveX control.
People from Mozilla China have recently pointed out to me the crypto-related issues in China. My understanding is that you can make Firefox do what you need for Chinese banking but it requires unintuitive configuration and/or hard-to-get drivers. I am hoping that sometime this year we will make improvements to make smartcards plug-and-play on platforms (like Windows) that support it. This will be a nice benefit not only for Chinese users, but also for any other smartcard users.
Significant changes have probably been made to the implementation since the NSPlugin implementation was dropped; the protocol may have become dependent on ActiveX-specific features/settings.
I don't know enough of the technical details to fully follow the discussion, but it looks like support might have been added to Firefox ("Status: RESOLVED FIXED"): https://bugzilla.mozilla.org/show_bug.cgi?id=478839
