Simply said: That's what diplomacy is about and it's useful. My own impression is that it's the urge to take a moral stance about everything that is new. And you have got to ask what purpose being all righteous would serve apart from giving the local public an occasion to feel smug.
There is no reason to think that it's an effective way to bring about change and even if Western democracies really had the power to remake other countries in their image, it's not entirely unproblematic to dictate (once again!) what they should do, even if it's apparently for the greater good.
What happened during the Cold War was very different. First of all, the two blocks did have diplomatic relations and you can find many interesting nuances (e.g. the way the People's Republic of China was treated), it's not like they did not talk at all.
Secondly, this was more about traditional power politics than a consistent moral compass. Everybody had allies that should have been unpleasant in light of their official ideology. Thus, the US could shun Cuba but cozy up to unsavoury dictators in Africa and elsewhere.
Of course, immunity is a sine qua non of diplomacy, a rule invented to move away from earlier practices like killing ambassadors and sending back their heads when you weren't happy about something. There is a very good reason it exists, especially between states that don't trust each other. Note that Western diplomats and international organisations also benefit from it and rely on it daily.