There's a simple reason Groundhog Day are inconsistent because what counts is the story.
writers Christopher Markus and Stephen McFeely believe that only the removal of the Infinity Stones creates a new timeline, meaning that Steve Rogers was Peggy Carter's secret husband in the MCU all along. This certainly explains why an elderly Peggy had photos of Steve at her bedside, but none (apparently) of her actual husband.
A recent interview with Tilda Swinton has hinted at just why there was all this confusion; it's because Marvel changed the rules partway through production. Swinton's Ancient One made a brief appearance in Avengers: Endgame, giving the Hulk an infodump on the MCU's temporal mechanics. It's one of the key moments in the film, outlining the basic rules and including a nifty visualization.
Swinton shot her original scene on a summer day, then a year later was called back for reshoots because an important plot point had been changed. According to Swinton, it was "all about that very, very important" visual timeline effect, and her revised lines stressed that the Infinity Stones had to be returned. Based on what she said, that dialogue was setting up Captain America's time travel plan at the end of Avengers: Endgame that leads him to Peggy Carter. Markus and McFeely have insisted Cap's ultimate fate was decided right from the first draft, but it looks as though the Infinity Stones idea was added in order to justify it.
It's frankly no surprise there's been confusion about how time travel works in Avengers: Endgame. Even the best time travel films play around with their rules in order to service the non-temporal plot, and in this case Marvel literally changed the rules late in the day in order to subtly rewrite said plot. There was no way such a last-second adjustment was not going to have a knock-on effect to the rest of the movie, even if Marvel probably didn't expect it to be highlighted so much by conflicting comments from the writers and directors.
That said, it's possible the issue will only be resolved further down the line. Mysterio is lying about his alternate dimension origin story. If Mysterio is telling even half the truth, though, it would hint that the MCU consists of countless branching realities. This relates more to Thanos' snap than it does time travel, but surely means the Ancient One was presumably over-simplifying in her explanation to the Hulk.
ing this, TV series for the Disney+ streaming service, exploring alternate MCU events. While it's riffing on ideas from the comics, this could be described as a product of different timelines. That would suggest the Russos are correct - and potentially even means the series could explore the new timeline Captain America created when he went back to the 1940s to live with Peggy Carter.
