You can read galnet ingame in your ship whilst not docked by looking at the left panel and selecting "galactic powers"
Which essentially launches an in-game browser completely locking you out of the ship's controls etc.
Also EDDI will read new articles to you as they're posted, without having to go to the Galnet page.
Yeah, unsanctioned third party add-on, but useful

Still, a third party addon fixing bogus game design decisions.
Lets be honest...ObsidianAnt is the ED story teller
Fact. Also I think he actually should be on Frontier's payroll as the best ambassador there is...
it's a bit hard to get everybody involved with the story when the playerbase is spread about an entire galaxy.
On the contrary. You could influence large portions of the playerbase in the way I mentioned earlier - by giving us npc conversations in space bars or at least comms chatter here and there. To be fair they did something like that when the first alien occurences started, npcs chatting about something strange happening in Pleiades and it was AWESOME. Too bad it was too limited in scope, the proper breadcrumb trail would be going to pleiades and talking with the locals, maybe getting a mission or two to search for something, or as someone proposed, a regular mission with an unexpected outcome of stumbling over something... The possibilities are there, they just need to decide and code it in game.
Instead as many others have said, we get an easter egg hunt, and only selected few with proper knowledge and resources are able to participate. I am fine with that though, I accept that there are much more smarter people than I am, able to figure it out much faster. While I would love to be able to participate, I am not hell bent on it. It would suffice if I could somehow be notified in game about that by means described above.
Season3 of core improvements, you are our last hope,
Obi Wan FDev.