I cant really bother to read the opinions of others regarding this as they are very long, but my personal opinions on it are as so:
Fates' story on all three routes is very poorly done. As the next game after Awakening, I feel it takes two steps back in regards to story presentation and execution, while having a pretty interesting premise. It seems frankly a bit opposite to Awakening's story, which had a pretty run of the mill premise with extremely well-done execution. I would chalk this up to the writers/artists/etc having to produce content for three different routes in what was likely a comparably short timeframe, not to mention how Intelligent Systems might have been split up on work between Fates, Awakening DLC, and SoV at some point, not even mentioning any other projects they might have been assisting at the time. Being able to romance and have children with who is presumed to be your blood related or functional siblings is kinda creepy, and the optimist in me thinks this was a byproduct of them not understanding the ramifications of a story mostly involving familial ties being in a game where your character can romance damn near anyone as a selling point.
Fates' gameplay is honestly rather nice on higher difficulties. Conquest on Hard Classic is painfully challenging but very rewarding, Birthright felt a bit too easy on Normal but could be enjoyable on Hard Classic as well. Haven't dived into Revelations yet but I assume its the same. The map design of Fates all around was phenomenal at points, especially that map with indoor/outdoor elements when it was used in Conquest, Azura sneaking around the map like she was playing a stealth game before she could meet up with allies. I think the gameplay of Fates' combat was a proper step forward from Awakening and its the only thing that keeps me coming back to it
Overall, isn't deserving of hate, or being considered as the worst game by any stretch, but it deserves a lot of the criticism it gets.