Here's the thing. Awakening was written by a mangaka, a really bad one at that. Since Awakening, IS had the itch to be considered "mainstream"? (either that or they desperately wanted to make the games "modern", so they looked for things that Japanese teenagers were into) so they began to hire people in the anime/manga sphere in order to give new life into the series. They stopped after Fates because, even then, they received negative feedback in regards to the story (when you bring on board the writer of fucking Senran Kagura, nothing is bound to go right).
3H was written by people in Tecmo Koei. They have only been involved in other musou games and nothing else. For what it is, it could have gone waaayyyy worse.
Even then, if we go back to genealogy, it was a simple game that never had any big factors to fuck up when it came to its story. So it's anime cliches were not as glaring. Not to mention how every game has at least one "anime degeneracy" quirk about it. Raven and Priscilla, Eirika and Ephraim, Cellica and Micaiah being completely idiotic and the plot gives them what they want regardless of their fuckups; Yune, the goddess of destruction being a loli. Those are the only ones that I can remember, I'm pretty sure there's more.
Most anime and anime-adjacent media (like jrpgs) changed notably from the 90s to the mid 2000s-2010s due to changes in anime trends. "Tales of" is another game series that had relatively less "modern anime shit" back in its roots like Phantasia or Destiny from the 90s-early 2000s, they were still very much anime but they didn't feel "as anime" as most people say FE or Tales of is today. Arguably these games have always been "anime" as fuck, just they follow stylings and tropes from the 90s era that most people argue is the "golden age" before the rise of moe and shit like that which is when anime became mainstream, and to the average viewer is not really seen as much today. Most people don't know or remember 90s anime past really normie stuff like DBZ, Sailor Moon, or Cowboy Bebop.
Also Arvis fucks his half sister and has two kids with said half sister, Seliph's main pairing is with his half sister Julia. FE has had degenerate incest before what you're talking about, and I never got that Raven and Priscilla were into each other that way. Raven follows an edgy avenger trope and Priscilla is supposed to be his foil to save him from his darkness by being gentle and kind to contrast him, the writers use Raven's passion for his lost family to turn him away from his pursuit of revenge and just be content with what he has now. The problem is Raven's story goes fucking nowhere despite him traveling around with the man he wants to kill, nothing comes from that ever so no one cares about Raven's story.
Eirika and Ephraim are more a weird reference with their signature weapons (Sieglinde and Siegmund) relating to a musical drama where a pair of twins separated at birth fall in love and fuck. I don't know how much IS knew about that or cared as JP likes to use random western fantasy/mythology names for no reason like Tyrfing, Ragnorak, Durandal, Vorpal Sword, Flamburge, or even good ol' Excalibur that have at best passing glance connections to their original origins or basically none at all. So I never bought into the FF8 incest twin meme being really backed by the story, are they close? Sure, but that doesn't equate to "They want to fuck" in the same way other anime-like media go for the "siscon" trope in a much more direct way.
FE has had ultra powerful lolis since FE1 with Tiki, FF6 and 8 also have powerful dragon lolis. Why? Who the fuck knows why this is a trend, it just is so Yune being a loli isn't that unusual within the scope of Fire Emblem. I'd also remind you that Tiki and Marth is a very common pairing, that Awakening emphasizes even more, so if any game is full blown loli bait degeneracy it is Awakening (because Nowi's existence), and then FE1/FE3 due to Tiki/Marth. I'm in the camp that Fire Emblem has always been about as anime as it is today just different time periods, and the only thing that really held it back was lack of technology/budget to really emphasize that like it does today during the time when JRPGs especially tried to add more "anime shit" into their games.
tl;dr: Fire Emblem has always been anime as fuck, we're just arguing if its good anime or bad anime at this point.