RE: Jaime. Shouldn’t we just asume that Kingsguard vows take precedence over the knighthood ones, if they ever come into conflict?

Well, you know what they say about assuming things…

But seriously, unless otherwise stated, it would be much more likely that the earlier binds the former, just as legal precedent itself means that older decisions are binding on future decisions. In this case, my contention is that, having sworn the oath of knighthood, Jaime is not in fact completely free to swear to “Defend the king. Obey the king. Keep his secrets. Do his bidding. Your life for his” in any situation where obeying the king or doing his bidding would cause him to violate the first oath.

To take an example that’s not too farfetched given events in ASOIAF: given that the oath of knighthood requires knights to “protect all women” and to “defend the young and innocent” should a kingsguard obey Joffrey’s command to beat Sansa? I would argue that Sansa’s ACOK chapters suggest strongly that any knight who obeys such a command is not a true knight, whether we’re talking about brutes like Boros Blount or Meryn Trant or the squeamish like Arys Oakheart. 

On that last Jaime point, perhaps you’re right under our own moral apparatus but I don’t believe even Eddard ever held that against Jaime, certainly less then the oathbreaking. Plus would it have made a difference other then throwing Jaime’s own life away alongside Lord Rickard and Brandon? All I’m asking is what effective resistance we should reasonably expect from Jaime given his position? Or Tyrion who noted that being born a Lannister tied him to their fate/destruction at the time?

Not just under our own apparatus – it’s also the case under the ideals of knighthood. A true knight is supposed to uphold their vows at all costs and no matter the consequences – which points to GRRM’s romantic/existential leanings. And the oath of knighthood explicitly states that:

In the name of the Warrior I charge you to be brave. In the name of the Father I charge you to be just. In the name of the Mother I charge you to defend the young and innocent. In the name of the Maid I charge you to protect all women.”

The Mother’s clause points to the fact that  Rickard and Brandon were innocent (and helpless, given their chains) until proven guilty; the Father’s clause reminds us that the laws of men and the laws of the old gods and the new state unequivocally that they had the right to a trial and killing them without one is murder; the Warrior’s clause demands that Jaime fight for the right no matter the odds. 

And yes, it’s not easy. As Jaime points out, there were dozens of knights in that room, many of them of great reputation, who did nothing, who put their oath of obedience above their oath of knighthood. But true kngihts are rare precisely because it is so difficult to put your ideals ahead of all practical considerations. Remember Dunk at the Tourney of Ashford and how rare it is to find a knight who remembers his vows; remember Brienne’s desperate fight against the Bloody Mummers or Jaime’s suicidal leap into the bear pit. 

Does Tyrion fall under the same purview for propping up the Lannister regime prior to the Purple wedding? I’m just genuinely curious if we’re working from the same standard here because I’m baffled as to what we could/should expect from someone in Jaimie’s position (who did do the right thing once upon a time and was vilified for it) while accounting for the fact that he was born a Lannister and ask what viable political alternative exits for him to resist for at this point?

I certainly think he does. 

Indeed, that’s the central tension of Tyrion’s arc in ACOK – we’re rooting for him to succeed against Cersei and Varys and Pycelle and Littlefinger, we cheer when he leads the sally from the Mud Gate to the cheers of “Halfman!” but at the end of the day, Tyrion’s success means that Joffrey stays on the Iron Throne.

And this is a point that GRRM hammers home again and again. Tyrion starts ACOK by proclaiming that he’s going to “do justice,” and he’s absolutely gobsmacked to find out that the smallfolk of King’s Landing hate him. And as much as he likes to blame everything on Joffrey and feel aggrieved, Tyrion’s his Hand of the King and doesn’t do a damn thing when Joffrey starts giving orders to murder innocent civilians or shooting starving people with crossbows. 

I would also argue, btw, that a big chunk of Tyrion’s ASOS arc is his realization of his complicity in this regime and his realization of what the regime is like when you’re no longer the man on top…

Now, it’s an open question whether Tyrion is going to reawaken to humanity as @poorquentyn explores in his ADWD essays, but I personally hope that part of that process is Tyrion realizing that it’s not enough to try to “soften the blow” but that one has to defect from the system of oppression and join Dany’s revolution in order to actually “do justice.”

As for Jaime, I think I’ve made my opinion clear on that point: Jaime’s hated because he stupidly refuses to tell anyone what he did and why. But in my opinion, Jaime should be condemned for not stopping the Mad King the moment Aerys gave the command to burn people alive without trial.