If I applaud that these turds lost their jobs after coming out as racists and neo-nazis in Charlottesville (and I do),
then I am not sure I have much room to object to this woman being fired for flagging a bird at Trump and his motorcade.
There are, however, a few differences that I see as significant:
1. Her action was expressing her opinion about Trump, not about an entire category of people. Unless Trump does his own ordering for this company, chances of her opinion of him having a direct impact on anyone is slim to none. The white supremacists, otoh, have outed themselves as the type of people who think other people should be second class citizens... other people who are very likely to be customers of the businesses. As a company owner, I would no longer trust them to be treating ALL of my customers with respect and/or providing good customer service to them.
2. As others have noted, virtually no one anywhere would recognize the woman from the photo - even if she posted it on her Facebook page. The white supremacists otoh were clearly identifiable. Customers & other employees could easily recognize them, and then feel very uncomfortable having to deal with them in the workplace.
3. Akima LLC was inconsistent in their policy enforcement. They immediately fired this woman for the photograph that neither identified her or the company; yet "a male colleague kept his job after recently posting lewd comments on his Facebook page that featured Akima LLC as his cover photo. She said this colleague was reprimanded for calling someone “a fucking Libtard asshole” on Facebook, but was allowed to delete the post and keep his job."
4. Akima LLC "told her that because Akima was a government contractor, the photo could hurt their business". If this company is telling the truth that they have reason to fear government retaliation in the form of lost government contracts - that
is a violation of free speech.