Skull: Fortress Knight
Since Fates treated clubs as equivalent to axes, I treated that as an excuse to treat Skull's weapon of choice, a bludgeon, as an axe. This worked out quite well, as the system I used gave Skull the highest HP out of all the Thieves and the second-highest Strength (he ties with Fox for the highest Defense), as well as the lowest Magic, Dexterity, Speed, and Resistance--pretty much a shoo-in for the Fortress Knight class, in other words.
Panther: Bishop
Panther has the lowest Strength and Defense and the highest Magic and Resistance, so I knew right away that I had to put her in a class that capitalized on the latter. She also tied with Mona for the highest Luck (I know Mona has higher Luck in Persona 5, but the system I used for translating stats to Three Houses gave them equal Luck) and has the highest Resistance out of all the Thieves. She also has pretty low HP and Speed, as well as below-average Dexterity. I treat access to healing spells as an aptitude for Faith, and the Bishop class requires high Faith skill and capitalizes on Panther's best stats. In addition, it renders her weapon of choice (a whip, which has no real equivalent anyway) irrelevant.
Mona: Trickster
Mona's strengths are in Speed, Luck, and Dexterity, tying with another Thief for the highest of the latter two (Panther for Luck, Violet for Dexterity).
He also ties with Violet for the lowest HP, and his Strength and Defense are both pretty low, albeit not the lowest. His Resistance is right in the middle and his Magic is above-average, though. This all being the case, I chose the DLC-exclusive Trickster class, which capitalizes on his best stats and allows him to use magic. The Trickster class requires skill with a sword and Faith, both of which Mona has aptitudes for in my system.
Fox: Hero
Fox was a bit of an odd case. He has the highest Strength and ties with Skull for the highest Defense, which would make him a good Fortress Knight, but I consider Skull a better fit for that class. He's also got low Resistance and Magic, so he's an obvious choice for a physical class. His HP and Speed are above-average while his Dexterity is below-average and his Luck is the lowest out of all the Thieves. While his preference for the katana would make a Swordmaster appear his ideal class, his Speed didn't strike me as high enough to justify making him one--plus I found Crow to be a slightly better fit for the class. As such, I made Fox a Hero.
Queen: War Cleric
Queen's preference for brawling, coupled with the DLC-exclusive War Cleric being the only brawling class available to women, made it pretty clear to me that she'd have to be either a War Cleric or some sort of spellcaster. She has access to healing abilities, which checks the Faith requirement for the class, too. Her stats were the deciding factor, though. While her Strength and Magic are roughly equal in Persona 5, relative to the rest of the Thieves, her Magic is superior by a sizable margin. Her Luck, Defense, and Strength are all below-average while her Speed and Dexterity are above-average (second-highest and third-highest, respectively). The War Cleric class doesn't capitalize on her high Speed, but it gives an adequate boost to her low Strength, which allows her to fall back on brawling against high-Resistance enemies, and also capitalizes on her high Magic and Dexterity while giving a sizable boost to her HP.
Oracle: Dancer
I couldn't find any stats for Oracle, which I don't find surprising, considering her role in battle. Her emphasis on support made her a natural choice for the Dancer class, though, as its special ability means that she'd be kept away from combat whenever possible, rendering her lack of stats irrelevant.
Noir: Warlock
As much as I wanted to make her a Warrior because of her use of an axe, her stats told me she was better off focusing on magic. Noir's Strength and Magic are both pretty high, but the rest of her stats are around average. Good Warriors need high HP, Speed, and/or Defense, and Noir just doesn't have those. There's also nothing preventing a spellcaster from switching to a weapon in Three Houses, so even if Noir would do more damage with magic than an axe as a Warlock, she'd still be able to use an axe as a backup just like Queen and her fists.
Crow: Swordmaster
Like Noir, Crow's got above-average Strength and Magic, though he's also got above-average Speed and Dexterity. Between his preference for swords and the aforementioned stats, I concluded that he was a good fit for the Swordmaster class, though I concede that he's still a bit slow for a Swordmaster. Frankly, he'd also make a decent Dark Bishop, considering his Persona's access to Curse abilities, which I treat as Dark Magic, though his merely above-average Magic means that as with the Swordmaster, he wouldn't truly shine as a Dark Bishop the way Skull shines as a Fortress Knight.
Violet: Assassin
Violet's another character with above-average Strength and Magic, meaning she could fit adequately into a spellcasting class. However, she has the highest Speed and ties with Mona for the highest Dexterity and the lowest HP, so I think she'd be best off in a class that capitalizes on her Speed and Dexterity. Since the Assassin class can't use magic without the help of a magic weapon, I concluded that the Trickster class was better reserved for Mona, meaning Violet strikes me as the better choice for the Assassin class.