Bullshitting is where you don't care about whether what you say is true. Your goal is to influence a certain way of thinking or feeling, and you just say stuff that you think will cause that in other people. Appearing to care about truth is not opposed to that, it's part of it.
I don’t think these mental states are in evidence for either of them. I think they’re both credibly earnest in their views.
(Frankfurt’s characterization of the bullshitter rests on not just the truth value being absent, but also on the bullshitter’s misrepresentation of what he’s “up to.” I don’t feel that either Zitron or Altman is misrepresenting what they’re getting up to.)