Warning: Contains SPOILERS for Shang-Chi and the Legend of the Ten Rings.
Fitting Phase 4 with the introduction of the multiverse, the inconsistencies have existed for years now. While they mostly don't damage the MCU's canon in the grand scheme, that hasn't stopped canon-obsessed viewers from trying to piece it all together.
In theory, Shang-Chi should be an easy movie to slide into the MCU timeline. It takes place after Avengers: Endgame and includes almost entirely new characters whose stories can be tailored to avoid conflict with the timeline. The general story of Shang-Chi does fit well in a post-Endgame MCU timeline, but the specific details it includes and references it makes are what will create some confusion. The film primarily focuses on Shang-Chi's life, showing him being raised by Wenwu within the Ten Rings organization, defecting from the group as a teenager, and spending the next decade living a normal American life until he's pulled back into his father's schemes. It is through this story, though, that Shang-Chi and the Legend of the Ten Rings becomes the latest movie to break the MCU timeline.
Shang-Chi and the Legend of the Ten Rings' problems come with breaking down Shang-Chi's life. He's suggested to be born in 1996 (or shortly thereafter), but he leaves the Ten Rings when he is 14 years old, which would be in 2010. Shang-Chi says that he met Katy soon after coming to the United States and has known her for 10 years. This moves the timeline up to 2020: two years after Thanos' snap and three years before Avengers: Endgame and The Blip. Taking this information at face value, it would mean that Shang-Chi would have to be snapped. The movie doesn't touch on whether or not that happened, but Shang-Chi would have to take place in 2026 for this to be true and line up. This would make Shang-Chi the furthest movie in the MCU timeline so far by a long shot. However, a reference to Shang-Chi being called Gangnam Style when he first came to America doesn't match this timeline, as the song wasn't released until after 2010.
There is another possible explanation for how Shang-Chi's post-credits scene that is the biggest hang-up. Unless one of Carol Danvers' superpowers is faster-growing hair, she should still be much closer to her short hair look in Endgame.
Both scenarios for how Shang-Chi works in the MCU timeline work on a macro level, but the micro details are really where it shows a brokenness. Marvel Studios has overcome similar timeline issues in the past, but that doesn't make them less frustrating for some fans. It could even create more issues moving forward depending on Shang-Chi potentially connects to other Phase 4 projects like She-Hulk. Ultimately, the second explanation presented here is the one that makes the most sense, Carol's hair aside, and lines up better with how Shang-Chi and the Legend of the Ten Rings presents the current state of the MCU in a post-Avengers: Endgame world.