I'm not sure I want to ever work with you. There are a lot of situations when with my coworker I discuss things in a way that could be misunderstood. This because my coworker have access to a lot of context (we work together) and they are well intentioned and able to extrapolate from the context my real meaning and belief. The general public doesn't have the same context. Plus, a third party could have a vested interest in representing my ideas under the worst light for me. So this is why I want to make some statement publicly, knowing the impact of my phrase, and use a different tone in private with people that know me.

And that's without touching the problem of public policies. Honestly speaking, some issues are generally too complex to be analyzed in a debate or in public speeches. So complex articulated analysis needs to be reduced and simplified. On some topic, it is possible to have a point of view that, when expressed, is a very valid one, but requires a lot of education to get buy-in from the general public. So if you are a politician what do you do? You could choose to use part of your consensus to push for a dividing policy and educate the public on why you are right. Are you could decide to wait, flow with the public, until you are ready to make your position public.

I think you're looking for an objective truth that just doesn't exist. People change their minds. People have different opinions on things from one day to the next, based on what they just read. People will publicly say "the right thing" while privately having reservations about it - and that's ok.

Now if they go round saying the exact opposite in private, and condemn their own public remarks, then there's a problem. But that's mostly not the case.