"Logic" suggests Bayesian analysis but you're working with too few bits. When you make an absolute-sounding posterior claim based on thin or non-existent priors, you risk losing sound inference in favor of pushing a preferred conclusion.
I'm disputing your absolute-sounding "Mozilla’s employees are fiercely liberal". Even if you define "liberal" broadly, are they all? Really, no moderates or righties? As I happen to know some, and so do other people, you seem to be using hyperbole at best, if not making things up.
Also your absolute, unhedged "If you have a conservative bone in your body, you are not welcome on the Mozilla campus." Again, counterexamples are known personally to me and others on HN such as @roca. So instead of persuading, you're exaggerating for some reason (to divide and conquer, to get sympathy, it doesn't matter -- the exaggeration is the point and it blows back, assuming you are actually trying to persuade anyone; perhaps you are writing not to persuade?).
Mozilla would have trouble with state law if they actively fired or demoted anyone over past political acts, per California Labor Law 1101 and 1102. Let's agree that is not the case.
That leaves subtler biases. You could be right, especially after I left, that anyone who is known to be "on the right" (conservative is almost useless as a clear political term) would face subtler kinds of hostility, skepticism, pressure. You are probably right about executives, but that's true at a lot of places. Anyone pushing buttons by boosting Trump at lunch or water-cooler time, wearing a MAGA hat, etc., would run into complaints and escalations.
But at this point we are far from your absolute, unqualified assertions about "are fiercely liberal" and "not welcome". See what I mean?
P.S. See https://robert.ocallahan.org/2014/04/fighting-media-narrativ... including all the comments. I'm not taking anyone's side there, but if it were as absolute and simple as you asserted, many righties would have quit too and we'd hear from them. If I missed such testimony, please link.