If you're in a minority in cabinet (and, if you're thinking at all, you probably are quite often) you must let your colleagues know about your concerns. However you mustn't say anything to undermine the agreed policy in public. You stand behind the decision. This isn't dishonesty in a broad sense; it's basic teamwork. Most voters have been part of a team in their lives and understand this well. A minister who thinks a policy is very wrong has the option to resign. If it's morally wrong or likely to cause serious damage to voters, that's what the minister should do.
"Cabinet responsibility" is therefore not a problem to voters. We get it. We would probably take against a minister who was disloyal in this way. We might even sympathise (while of course – for we are only human – enjoying the PM's discomfiture) when a dissenting minister briefs the press anonymously.
This is one reason why the recent Conservative Party leadership election has been so problematic for the government. Like a primary in the US, it has provided endless ammunition to the opposing party as candidates tried to differentiate themselves. A bit of Blue on Blue was inevitable. It's an index of the poor quality of the Reds that no more serious damage was done. The fact that modern Leftists seem to look more for opportunities to insult their opponents than to engage them in reasoned argument is a gift that keeps on giving.
Some interesting data emerged – for example as to the COVID 19 lockdowns – but the fact that the people claiming they'd opposed them were in Cabinet at the time – and didn't resign – prevents them gaining the moral high ground. We're still left feeling betrayed that the "the science is clear", "there is no alternative," "Save the NHS" propaganda was a lie, of course. It just doesn't make us love the people claiming they always knew. And of course it's embarrassing data HM Opposition can't exploit, because its stance on democidal lockdowns was consistently "sooner, harder and for longer".
As a supporter of Austrian economics and a proponent of minimal Government/maximal Liberty, I couldn't take seriously the various candidates' sloganising about free markets and free societies. The Johnson regime was wrong on pretty much everything but Brexit in ways that suggest that – though the Left can't win an election in Britain because most Brits are conservative – they're winning all the arguments in the corridors of power. Until a "conservative" government actively purges the Deep State including the Civil Service, the police, the NHS and the education "blob", it will always now be conservative in name only. To these "Conservatives", "Liberty" is a nostalgic name to call your daughter, not a principle to die for.
On such issues, for example, as Net Zero (the ultimate cause of the current cost of living crisis; the proximate cause being the actions of a Russian leadership emboldened by our suicidal energy policies) this Conservative Government is to the left of reality itself. The Deep State in Britain (the permanent establishment that is merely fronted by elected politicians) is to the left of the Chinese Communist Party. It doesn't care who the Prime Minister is. It doesn't need to.
So no, I can't get excited about a change of PM. It's as interesting and important as changing the figurehead on a tall ship. The UK Ship of (Deep) State will sail on serenely to the nation's doom. Liz Truss might be slightly more aerodynamic than Bunter Johnson, but not enough to make a difference to a ship so vast, clumsy and barnacled.
Nothing has changed and I see no reason to hope that anything will until it's too late.