If the split is clean, and International ANSWER as a whole (coast to coast) is taken over by the west coast (+ Brian Becker) WWP split, then relatively little will change. La Riva and the Becker brothers still hate the Dems, and I don't believe for a second that people with such long tenures as communist-cult-bosses are suddenly going to embrace an open principle of organizing.
That said, I don't think the split is clean. From my somewhat-limited perspective, it looks like the WWP split has resulted in different branches of at least two of their front groups, International ANSWER and the International Action Center, being partially controlled by the NYC-based WWP, and partially controlled by the ex-WWP in California. Maybe I'm wrong, but I predict that means things are eventually going to get real ugly. No group like the WWP gets along happily with their ex-members. Can they successfully manage a joint organization with them? I doubt it.
Here's what'll most likely happen: for the summer, the US gets divided up like the world at Yalta. The NYC WWP folks do the International ANSWER organizing for the DNC and RNC conventions; the SF folks support these from afar but largely get froze out. The folks from California who remain in the WWP get treated like gods and invited to speak on the East Coast; the ex-WWP doesn't. A few show up for the DNC / RNC and they're subtly made to feel like second-class citizens. Shortly after the January 2005 inauguration of Bush or Kerry, you'll have two separate ANSWER organizations.
Along the way, the WWP's going to ensure they get everything they're able to grasp. I predict the SF IAC is forced to change its name by mid-2005 after some on-the-down-low but nasty legal threatening from the WWP's very effective Partnership for Civil Justice. If the WWP can keep control over the West Coast's 501(c)3, the Progress Unity Fund, they will, and the ex-WWP members will be S.O.L. for cash - it all depends on which side of the split keeps at least two of the three legal directors.
Already the ways to donate on the International ANSWER site are divided up in a messy patchwork - in places, through their fiscal sponsorship with Alliance for Global Justice, in others, to the NYC-based Peoples Rights Fund, in the 'West Coast ANSWER' section, to the Progress Unity Fund. Do you think whichever coast controls that website is going to be able to resist trying to send a bit more funding their way? And as for the IAC - that's also big money and big reuptation. All of a sudden the main New York City IAC isn't linking to the SF IAC.
By the end of 2005 at the absolute latest, you're going to see a new WWP-style party composed of the ex-WWP members plus everyone they can draw in. That or they'll just try to take over what's left of the Freedom Socialist Party. They'll put out a paper as often as they can.
Unfortunately, I don't predict any public airing of the dirty laundry, except by word-of-mouth gossip and rumour. The WWP is pretty silent about its internal life. As much as I'd love to see the WWP-equivalent of a "Hate Communism, Hate the Spartacist League" series of rants, it probably won't happen. My curiosity will have to go unsatisfied.
For the 'movement' the whole thing doesn't mean much. The DNC & RNC protests aren't dominated by the WWP, and their occasional anti-occupation demos have petered out anyway. It just means that ANSWER on the West Coast won't be as actively encouraging a vote for the WWP as ANSWER elsewhere.