A search for "class timeline"
on the forums yields multiple results if you wish to try to track class timelines in a spoiler-saturated way.
The greatest problem with closely intertwining class stories is that it would force the game to dictate events that should be a player's decisions. If my Knight does something that impacts the Inquisitor line, the Knight's LS/DS/alternate solution decision has to be arbitrarily set by the Inquisitor writers when they're writing their side. Not okay.
However there are multiple crossovers and perspectives of the same unchangeable faction and planetary events.
There's significant reasoning/overlapping events between the Sith Warrior and Jedi Knight in Act 3, though due to the fact that the NPCs in each line aren't talking to each other, you aren't likely to realize it until you've played both lines. The NPCs aren't coordinating, but the writers clearly were.
Companion crossovers happen in several class conversations; I won't spoil those, but you'll find that Balmorra and Nar Shaddaa as character background locations are hotbeds of crossover activity.
The Empire's loss of Balmorra becomes hilariously clear if you note the pattern from playing Inquisitor, Bounty Hunter, and, to a lesser extent, Sith Warrior.
The Agent's recon during Act 3 has a number of blink-and-you'll-miss-it references to other class lines. This is Intelligence, after all, and they're keeping an eye on the situation.
The Consular gets unique insight into the planetary situation that the Empire classes knew about Balmorra.