These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Art-Style Dissonance: Starting with 3, the series became much more brightly colored in general, including quirky non-human sidekicks (Especially Teddie). However, the game is still not afraid to mention characters dying (in sometimes gruesome ways), show enemies that heavily resemble naked women in disturbing contexts, or even touch upon themes like impending death and apocalypse cults. In fact, the series has arguably been getting more graphic as it goes on, with Persona 3 and 4 being rated "M", whereas the first three only got a "T" rating. (The first also got a K-A rating, but that was a heavily Macekred version)
Broken Base: With the main series, due to its popularity overshadowing it and everything else Atlus makes. There are those who actively dislike the spin-off and its fanbase, viewing them as Johnny-come-latelies who can only enjoy watered-down gameplay and thematic compromise. Simultaneously, some fans are only fans of the spin-off and dislike the main series for its stagnant, recycled "order vs. chaos and both are jerks" plots, flatter characters that contrast heavily with the spin-off's heavily character-focused narratives, and its archaic difficulty and gameplay. There are those who enjoy both, but the two series are different enough from one another that there's less overlap than one would think.
The Persona fanbase itself has suffered its own break, mostly between the fans of the first two games and the fans who jumped on to the series at or after 3. The first two were much more heavily tied to the original Shin Megami Tensei franchise in plot, style, and gameplay than those after 3, where the Dating Sim elements began to enter the mix and the Tarot Motifs became much more prominent, and possessed shared elements that have, if not totally been abandoned, then at least somewhat sidelined following 3. (Philemon and Nyarlathotep being sidelined is a common example.)
Finally, there's the substantial-and-growing portion of the fanbase that's simply tired to the bones of Atlus constantly adding spin-offsto the spin-off for a quick buck and want the series to progress, given that Persona 4 came over half-a-decade and two console generations ago. And while Persona 5 has now been announced, so has Persona 4: Dancing All Night, adding fuel to the fire even as it addresses their core concerns.
Continuity Lockout: Averted - every game is essentially a standalone title. If a player wants to start at Persona 4, for instance, they have nothing to lose but a few cool Mythology Gags. The only game that has a true sequel is Persona 2, and even there much time is devoted to explaining the events of the previous one for newcomers. In fact, since the original never officially left Japan until the PSP remake,Eternal Punishment was a sterling example of avoiding this. The idea of a completely different adventure that had happened off-screen, leading up to the innocent sin, actually intrigued a lot of North American players.
First Installment Wins: Averted - The first game was only a cult classic at best, and has not fully enjoyed the gains of the breakaway success of the series following 3 and 4, partially due to their drastic differences is story, style, and tone.
Gateway Series: Persona 3 and 4 introduced many fans to the Shin Megami Tensei franchise. That said, just as many fans of the Persona series are not fans of the rest of the franchise.
Never Live It Down: The 10 month delay of Persona 4 Arena in Europe gets brought up every time the series is discussed. Regardless of the change in circumstances for the franchise since thennote Namely, Sega's 2013 purchase of Atlus meaning that Sega UK are now publishing Atlus games in the region as opposed to different publishers on a game-by-game basis, the EU fanbase still holds a grudge. Other titles also coming out late didn't help.
Sequel Displacement: How many people knew of Persona before the third or fourth games? For that matter, it's rare to meet a Western Shin Megami Tensei fan that wasn't introduced to the series by those two games.