The advice never to resign, never to apologise is good advice - but the reason for it is misunderstood.
The reason is not because then things will work-out better - that is not knowable, outcomes are not controllable.
Part of the reason is that resigning and apologising is exactly what 'they' want you to do - and that fact, in and of itself, ought to be sufficient evidence that resigning and apologising are a bad idea.
However that resignation and apology are what is wanted leads onto the question of exactly 'why' the secular Leftists - i.e. the mainstream socio-political Establishment of all 'parties' - so much want their victims to resign and apologise?
The answer is related to the underlying objective of the Establishment - which is to lead the world (first The West, then everybody else) into self-loathing, despair, implicit suicide, and ultimately chosen damnation.
(Our situation is one of spiritual warfare.)
Given that PC witch-hunts are primarily directed against those who tell the truth - resignation and apology means that the victim publicly repents his Good action.
To do something Good, and then to repent it - is actually worse than doing nothing; because it teaches (with the explicit endorsement of the victim) the public lesson that Good is actually evil.
Un-repented evil is, of course, the main weapon of the secular Left (by moral inversion they re-label evil as good, ugliness as beauty, and lies as truth) - but repented-Good is even more powerful a weapon of corruption than un-repented-evil.
This is also why most PC witch-hunts are directed against those of 'liberal' views, especially those who broadly favour the sexual revolution - rather than against those who have strong and primary religious convictions.
The witch-hunting Leftists know that other Leftists can be relied-upon swiftly to cave and capitulate.
This is because secular Leftist/ sexual revolutionaries/ 'liberals' (whether or not they term themselves socialist, democrat, conservative, republican, libertarian or alt-right) are all very weakly motivated when it comes to moral principles.
Secular principles are essentially expedient, this-worldly, and orientated towards hedonic goals: the enhancement of pleasure and minimisation of suffering in life. Such people can easily and quickly be pressurised into 'selling-out' - by simply piling-up the threat of disincentives.
So - when the chips are down (as opposed to their theoretical boasts or even sincere intentions) the secular/ liberal/ leftist/ sexual revolutionaries among victims of PC witch-hunts have almost all, and rapidly, capitulated - and done exactly what was wanted of them: resigned and apologised.
They may talk tough before the fact, they may say they won't capitulate - but, in fact, they do.
It is pretty much only those of strong religious faith who ever stand firm and refuse to apologise or resign; and this is simply because real religious motivations are much, much more powerful than secular motivations.
This is just a fact of human nature - known for centuries (or millennia).
And this is why a secular backlash against secular Leftism will not be effective. Any potential leaders will be picked-off sequentially, as and when they threaten to challenge the core agenda.
When things get tough - people who have rejected the divine will not hold the line, and they will capitulate.
Which is why there must be a spiritual awakening, a religious revival: nothing else can work.
Of course, real religious faith cannot be had merely because it gives strength of motivation - rather, strength of motivation is - or can be - a consequence of real religious faith. Strong faith is based upon knowledge of truth; and not on any kind of expediency or hoped-for this-world consequence.