This professionalism thing is most definitely a recent development. It's a child's idea of how adults are supposed to behave: super serious, cause this is super duper important adult stuff we have to do.
If a middle-manager and a lower-level coworker (like a secretary) were going out, and they started having a lover's quarrel in the middle of a serious business meeting, do you really think that's appropriate? Do you think they'd still have their jobs the next day? It's highly egotistical/narcissistic to put your own personal drama ahead of the business at hand, but of course, we're living in yet another me-decade so it just seems normal to bring your baggage into the board-room.
If a high-ranking naval officer was screwing a lower-ranking officer and, in the middle of negotiating some tense situation in the Straits of Hormuz, the lower-ranking female officer starts bitching out the officer, do you think that's appropriate? It's wrong on multiple levels, starting with raising questions about proper chain of command vs. nepotism vs. exploiting a power-imbalance.
You're damn right it's important adult stuff and that kind of behavior is selfish, irresponsible, and childish. There's a time for being responsible and a time for personal stuff. Keep your personal stuff for your off-hours.
The only reason it gets a free pass is that it's showbiz. Fantasy version of reality. And in JJ's case, he didn't want to let the films breathe enough to have real character-building moments so he has to wedge them in the middle of one long Transformers style chase-scene.
It's simply not the same as the kind of thing we saw in TOS because the pace was nowhere near as break-neck.
The reason there's as much inter-crew romance in Trek is because there doesn't seem to be anything interesting for civilians to do if they aren't a member in Starfleet. So at times it feels like everyone within Federation society is a fellow member of Starfleet and so it encourages more of an informal lifestyle overall, despite attempts here and there (like Wrath of Khan) to establish more pomp and circumstance. But in most cases, the relationships were back-story (Decker and Ilia and #1 and Troi were exes). The active relationships never ever worked, IMHO. It was better to have tension without it ever leading anywhere (like between Picard and Crusher). Having leads hookup like this is best left for cheap fan-fiction. It's too convenient and lazy.