That video ("Mozilla is Not Trustworthy") is remarkably inarticulate and inchoate all in pursuit of something we don't need to do in the first place -- trust Mozilla. And Mozilla certainly doesn't owe us.
Software freedom (the freedom to run, inspect, share, and modify published computer software) means we don't need to trust Mozilla's free software because we have permission to inspect the code to see what the software does, change the code if we don't like what the software does, distribute the improved software (or a verbatim copy at our choice) even commercially, and run the software anytime we wish for any reason. These principles place us in control of our computers to the extent we're willing and able to put in the work. We can even hire other people to do this work if we don't do the work ourselves.
Lunduke complained about incorporation and non-profit status but never articulated an argument explaining how these things are a problem. Around 7m53s he said this "doesn't make them [Mozilla] untrustworthy" leaving me wondering why this was brought up in the first place. He consistently mispronounced the word "Mozilla" as "Motzilla" (there's no "t" in their name), and directly contradicted his own thesis (around 6m30s) in neighboring sentences: "This is not an opinion on my part. I guess that my opinion is that they're not trustworthy based on these facts...". He did that again in his own ignorance of the terms "foundation" and "corporation" around 7m where he seemed to have a problem with the difference between what he read into the terms he didn't define versus what he described to be the case (thus vaguely complaining that Mozilla made money and published free software for hire). I think it comes down to not having a good argument to raise in the first place but feeling a need to say something about a situation he found irksome. But I think his disorganized view built on a non-issue is typical of the published reaction to this situation.
This entire kerfuffle comes off to me as manufacturing a controversy out of very little. The main beneficiaries of this indignance are the software proprietors -- organizations that make nonfree browsers you can't trust because you never really know what they're doing when those programs run.
It's telling that vanishingly little of the commentary on this situation brings people to understand what software freedom is or how its practical consequences read directly on this situation by explaining how the other programs to do the same job (mostly nonfree user-subjugating programs) are not alternatives at all because they don't respect a user's software freedom. It's not clear how this issue with Looking Glass (the Firefox add-on in question) rises to something more serious than a bungled PR effort and poor communication from Mozilla. Source code analysis shows that Looking Glass did nothing unless activated and that add-on was off by default; hardly something to get so worked up over and largely a purposefully-missed opportunity to teach people about software freedom.
There's no reason to limit this examination to web browsers. Justifying use of any nonfree browser in light of security problems hinges on trusting the proprietor (which you should never do) precisely because those programs are nonfree. Users don't have other information on which to make an informed decision and the information they have is inadequate to make an informed decision. These browsers are also published by known NSA partners. There's no good reason to defend switching to any nonfree program to do any job, particularly if you're going to have a discussion centered on privacy and security.
I see the lacking discussion on this topic as a consequence of pushing for "open source" instead of insisting on software freedom. Open source development methodology was founded to separate the ethics-based principles on which the free software movement is based (the free software movement is a social movement) from the practical outcome of software freedom -- lots of useful software -- while talking chiefly to businesses about the gratis programming labor those businesses can use. This approach purposefully skips past an ethical understanding of how to treat people with regard to computers. This approach requires talking at length about this situation without drawing users' attention to what software freedom is or how it matters. But there's no substance in that approach so proponents raise ill-formed non-issues (with a heavy dose of entitlement ("Mozilla has to prove to us that they are worthy of our usage") to make it seem like Mozilla has become a persistent problem instead of seeing a long-time free software publisher make a relatively minor communication mistake that posed no threat to Firefox users. Quite the contrary is the case: we can and should continue to run and build new programs on Mozilla's free software just as we do with any other free software. Thanking them for their work and not taking an entitled attitude is also right and proper.