No its not perfectly socially acceptable, in contrary. Rude is the best description, be it personal or professional life.

When I see such person who simply can't resist looking at their displays during conversations, I know I am seeing a hard addict with host of other attention disorders. And the fool is feeding those, actively making them worse for some ultra short dopamine kicks that keep getting shorter till they make new baseline.

Not a stellar person in any meaningful way, rather an addict or an asshole. So much for perfectly acceptable.

Are we talking about momentarily checking if there's an important interruption and continuing with the conversation? If so, I'm confused as to why you possibly think it's unacceptable and rude.

I can see how this could be considered rude in a very formal setting, or when matters of high importance are discussed and uninterruptible focus is a must. But for most casual situations, I perceive glancing at incoming notification as normal. Assuming this happens reasonably infrequently, of course - that is, a glance in a while, not constant checking every other minute.