Back when Grand Theft Auto 5 and its multiplayer component were still fresh, Rockstar was seemingly intent on weaving the two together and having them occur in a shared fictional universe. Officially, the events of GTA Online took place a few months before the storyline of GTA 5 (meaning post-North Yankton). However, since then, the game expanded in ways which conflict with this canonicity, raising the question of whether the two modes still share a universe?
The initial set up was that time in GTA Online didn't really move forward, at least not in the traditional sense. Basically, the game would take place in 2013 perpetually, always a few months prior to the in-universe beginning of GTA 5's storyline following the prologue which washes Trevor, Michael and Franklin together. A number of references in game are made to maintain this continuity.
Early on in your progression through GTA Online, you meet Ron and Trevor who play central roles in the story mode. Neither make any mention of events that take place in the story, precisely because they haven't happened yet. Trevor is still living his (comparatively) quiet life as a criminal drug addict just as his has ever since the North Yankton job and up until learning that Michael is still alive and kicking.
The player also eventually hooks up with Lester Crest, another major character in story mode. It is assumed that players go through much of Online's progression "before" the story events occur, since in a cutscene prior to the jewelry store heist in the storyline, Lester refers to the GTA Online protagonist as a possible crew member, but then dismisses the idea calling them "too unpredictable" (which is funny because (1) players would go on to conduct heists in Online and (2) the average random player is indeed incapable of successfully completing a heist).
All of this suggests that GTA Online does indeed occupy the same timeline and fits in neatly prior to the events of GTA 5. However, certain discrepancies have popped up since launch way back when.
Firstly, the huge amount of DLC released since 2013 has made Online much more content-rich - where did all those flashy vehicles disappear to? Why can't Franklin own a lowrider, for example? Why can't the crew make use of weaponized vehicles?
Another factor is the increasing absurdity of certain updates.
The Cunning Stunts DLC and its spin-offs completely shed the pretense of realism by suspending huge death-trap race tracks in the air with spinning floating pipes and checkpoints which turn one vehicle into another in a puff of colorful smoke. None of this would fit GTA 5's much more realistic setting.
Then there are timeline discrepancies.
Agent 14, in more recent GTA Online content, makes verbal indication that the year is 2017 in GTA Online, meaning not only does time indeed move at a realistic pace, but we've long left the events of GTA 5 behind - however some notable differences are present. Both Lester's factory and the O'Neill ranch are untouched, as they should be prior to the events of the story, but (minor spoiler) both get visibly damaged during the course of GTA 5.
Sure, one could say they were fixed up and restored - but to a completely identical state? Not to mention, this doesn't explain that if GTA Online time moves realistically and thus overlaps with the story mode while the latter lasted, there never was a state when the damage to these buildings was indicated in Online.
Did we just time-leap from a stationary 2013 to a stationary 2017? Things don't add up.
Of course, you can just put all this down to simple oversight on the developer's part, however only minor attention to detail and basically zero extra effort would be needed to clear up the lore. They could simply swap out assets with those already present in story mode, representing the world after the story is over, and say that time moves normally in Online. Or they could have had Agent 14 refer to the year as 2013 - though this still doesn't explain the DLC issue.
Another, seemingly even easier solution, is to simply state that after a certain point - say, Heists - GTA Online ceases to be canon in the game storyline so that it doesn't conflict with the established lore and timeline. This could be cleared up with something as small as a single Tweet from the official Rockstar account and be done with. This may seem like an insiginifcant and minor gripe to some, but many fans of the game are engaged by the storyline and would like to see this detail cleared up.