I think the severity of this can be overstated. I'm always suspicious of stories that quote forums, mainly because I've been on enough of them to know there are always lunatics of one stripe or another lurking there (though admittedly not to the degree displayed in the article), and using them as emblematic of the site as a whole is never wise. I also think the link between Gellar and the Tea Party might be being overstated by Burghart. I'm not sure attending one state-wide Tea Party Convention makes her a bridge between them and the EDL, though the fact her talk was entitled "The Muslim Threat" makes the people like Ross Douthat claiming the Tea Party are all about fiscal discipline look pretty foolish/wilfully blind. Plus, I'm pretty sure the EDL would be crowing that they have the support of "Durham University academics" if I so much as nodded at them in the street, because that's the way these people always work.
Even with all those caveats, though, this is unquestionably pretty worrying. A direct link from EDL to Gellar to the Tea Party concerns me precisely because Douthat and company are so busy arguing the group is reasonable and responsible, and it's just that vicious liberals want to paint them as racists. Providing cover to this crap isn't their goal (it's just the standard "if liberals hate it there must be something wrong with it" line the American Right has been pedalling for decades), but it's certainly liable to be the result.
At this point, it's pretty clear that those arguing the Tea Party are merely concerned about deficits and public spending are deliberately ignoring the elephant in the room. You can argue the main interests of the Tea Party are bigotry-free. You can argue there are plenty within the group who despise Islamophobia and anti-immigrant feeling. But at this point, it's time to acknowledge the elephant in the room: Tea Party bigwigs (including Congressman Steve King) are paying for known bigots to show up and talk about why their bigotry is something the group should all get on board with. A group which silently tolerates such sickness in their ranks is no better than one that endorses it, something Gellar herself would agree with.
So long as that group were Palestinians, obviously.