Harry Potter and Fantastic Beasts are set in the same world and though characters will likely never meet, it's fun to think about how they'd interact.
The Harry Potter and Fantastic Beasts franchises feature a wide range of memorable characters. Friendship is a prominent theme in both franchises; the Potter movies center around the golden trio and the Fantastic Beasts movies are driven by Newt's relationship with his beasts.
While the franchises are set in the same universe, the Fantastic Beasts movies are set years before the events seen in Harry Potter. This means that some of the characters from the two franchises have never (and probably never will) come face to face on screen. Newt and Hagrid would certainly bond over their love of magical creatures while Leta and Bellatrix Lestrange would certainly clash.
Arthur and Jacob may not have a whole lot in common on the surface, they're from two completely worlds after all, but they could certainly be friends. Arthur is a wizard who has a keen interest in the Muggle world and Jacob is a Muggle fascinated by The Wizarding World. While some Weasley moments were left out of the movies, Arthur is still portrayed as a loving and dedicated father who's incredibly curious, yet clueless about Muggles.
Arthur would surely have a whole list of questions to ask Jacob, just like he did when he first met Harry. The two characters could learn from each other about their respective worlds and perhaps Jacob could even educate Arthur on the function of a rubber duck.
Hagrid and Newt have a shared love of magical creatures and both have a firm friendship with Dumbledore. Hagrid owns many creatures across the Harry Potter series, including Fluffy the three-headed dog, Buckbeak the Hippogriff, and Norbert the dragon, while Newt has a whole menagerie of creatures in his suitcase. Also, both Hagrid and Newt were expelled from Hogwarts which is an experience not many others have had.
Hagrid is bumbling but loveable, two traits he shares with Fantastic Beasts protagonist, Newt. It's not impossible that the characters may cross paths in future installments of the prequel series and could certainly form a friendship. After all, Newt travels around the world in his career as a magizoologist and fans will remember that Aragog the acromantula first came to Hagrid in the pocket of a traveler...
Voldemort and Grindelwald are the main antagonists of the two franchises but they're both far too self-absorbed to become allies. They are both power-hungry and ruthless; but, where Voldemort uses fear and intimidation to gain control, Grindelwald uses charm and manipulation. At this point in time, there are still many unanswered questions about Grindelwald but it's already clear his villainy is enough to rival Voldemort's.
The two characters do actually come to face to face briefly in Harry Potter and the Deathly Hallows with Voldemort visiting Grindelwald in prison. In the books, Voldemort actually kills Grindelwald when he refuses to divulge the location of The Elder Wand which confirms an alliance would never work between the two.
Neither of these would be particularly focused on 'friendship' but they certainly have a lot of common views. The Dursleys have a deep hatred for The Wizarding World, their ignorance manifesting itself through their abuse of Harry.
Mary-Lou also despises witches and physically abuses many of the children in her care. Mary Lou's treatment of Credence actually mirrors The Dursleys' treatment of Harry. If The Dursleys had been around at the time of Fantastic Beasts, they probably would have found themselves aligned with Mary-Lou and the other second salemers.
Sweet-natured Queenie Goldstein and stern Severus Snape are almost polar opposites. One of Queenie's main focuses is love and her relationship with Jacob is of the utmost importance to her. While Snape is actually driven by love too, his admiration for Lily remains hidden and unrequited.
Despite coming good in the end, Snape is often cruel and severe with his students while Queenie is always ruled by her heart. Although the two characters share the power of Legilimency, this is actually a factor that would work against a friendship here. While Queenie would probably find this common attribute delightful, Snape would be less than impressed. He would hate the idea of another person being able to read his thoughts and uncover his secrets and Queenie isn't known for being discrete.
Hermione and Tina are both moral and pride themselves on following the rules. As time goes on though, both Hermione and Tina break the rules for the greater good. Hermione makes a stand against Umbridge along with the other members of Dumbledore's Army and Tina disobeys Picquery in order to help Newt.
Hermione is often seen getting Harry and Ron out of perilous situations too, just like Tina does for Newt in Fantastic Beasts. While both women do like to be in charge, they would find a lot to agree about. Finally, as Hermione is Muggle-Born, she could teach Tina more about Muggles which could help her to bond with her potential brother-in-law, Jacob.
Despite being related (through marriage), these two women don't share a lot of common ground. Bellatrix Lestrange was Voldemort's best lieutenant; she is utterly deranged and most of her decisions stem from an attempt to impress her master. Leta is more independent and loyal and her guilt over her brother's death is a driving force for the character.
Although they were both sorted into the same Hogwarts house, the two characters would more than likely be enemies. Leta tries her best to distance herself from her family whereas Bellatrix embraces the Black and Lestrange family values. If these two ever came face to face, a bitter duel would probably ensue.
Neville and Newt are both unlikely heroes and both value friendship and honesty. Over his time at Hogwarts, Neville becomes passionate about magical plants and becomes a skilled Herbologist. Neville seems to feel more comfortable around plants than people, while Newt is more at home around animals.
Neville and Newt were both outsiders during their time at Hogwarts so may find an understanding with the other. These two introverts might form a bond through their shared love of nature and could teach each other more about their own interests.