Given Allister's love for Ghost - type Pokemon which are often associated with the unknown and mystery, and Bea's focus on Fighting - type Pokemon which represent strength and directness, their personalities could clash at first. However, as they get to know each other through their shared love for Pokemon, they would find common ground. Allister might share his insights about the more ethereal aspects of Pokemon battles, and Bea could show Allister how to be more confident in the physical aspects of battling, creating a harmonious relationship in the long run.
In some fanfictions, the theme of discovery is present. They might find a new type of Pokemon or a hidden power within their existing Pokemon. There could also be a theme of mystery, for example, if they encounter a strange phenomenon in the Pokemon world that they need to solve. And of course, the theme of loyalty between them and their Pokemon is often explored, showing how their Pokemon support them in different situations.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). There are often a lot of Pokemon fanfictions there, and you can specifically search for ones involving Bea and Allister. Another option is FanFiction.net. Just use their search function and type in the relevant keywords.
Paul's highly competitive and somewhat abrasive personality would likely be a contrast to Reggie's calmer and more diplomatic nature. In a fanfiction, this could lead to some interesting exchanges. For example, when they are in a Pokemon battle, Paul might be overly critical of Reggie's strategies, while Reggie would try to see the good in Paul's approach. As they spend more time together, perhaps on a journey or in a Pokemon training camp, their personalities could start to blend. Reggie might become more assertive under Paul's influence, and Paul could become a bit more empathetic thanks to Reggie's example.
Red's introverted nature might initially make Cynthia do most of the talking. But as time goes on, Red would contribute his own unique experiences from his adventures in Kanto. Cynthia, being so passionate about Pokemon, would be eager to hear about different regions and how training might vary. Red would be impressed by Cynthia's vast knowledge and her calm demeanor in difficult situations. Their personalities would complement each other, with Cynthia's outgoing confidence and Red's understated strength creating a balanced dynamic.
Ash is very adventurous and has a strong sense of justice. Rukia is also brave and has her own moral code. Their personalities would likely mesh well as they both strive to do what's right. Ash might be a bit more impulsive, while Rukia is more calculated. So, Rukia could help rein in Ash's impulsiveness at times, and Ash could encourage Rukia to be more spontaneous.
Perhaps a story where Allister is having trouble with his confidence in battles, and Bea decides to train him. She shows him new fighting techniques for his Pokemon, and in return, Allister teaches her how to better understand the more mysterious aspects of Pokemon battles. This way, they both grow as trainers and form a strong friendship that helps them face tougher opponents in the future.
Ash is very determined and passionate about Pokemon. Gwen is intelligent and has a strong sense of justice. Their personalities could interact in a way that Ash's enthusiasm rubs off on Gwen when it comes to exploring the world of Pokemon. Gwen's rational thinking could also help Ash make better decisions in his Pokemon battles and adventures.
Pinkie Pie would be all over the Pokemon, throwing parties for them and making new friends easily. The more energetic Pokemon like Charmander or Cyndaquil would probably be drawn to her fun - loving nature. She would introduce them to all the fun things in Equestria like parties and games.
Ichigo is often headstrong and driven by his sense of justice. Unohana, on the other hand, is more reserved and has a deep well of knowledge. Their personalities would likely create a dynamic where Ichigo might initially be a bit frustrated by Unohana's calm approach, but gradually learn to appreciate it as he realizes the wisdom behind it.
Naruto is very outgoing and determined. Saphira is wise and powerful. Naruto would probably be in awe of Saphira at first. He'd be constantly trying to impress her with his ninja skills. Saphira, on the other hand, might be a bit reserved but would gradually warm up to Naruto's enthusiasm.