Pandora
Pandora persuaded Regulus to accompany her to attack Elior Forest and succeeded. Also, Regulus sees Pandora as a higher ranked member of the Witch Cult, unusually referring her with "sama". But no matter how great his respect for her is, Regulus was more than willing to blow her to pieces when she kindly asked him to spare Petelgeuse's life.
Petelgeuse Romanee-Conti
Regulus seemed to be acquainted with Petelgeuse and was a fellow member of the Witch Cult. Regulus felt nothing but scorn and dislike when it came to Petelgeuse, referring to him as "abominable" on many occasions. Petelgeuse entrusted Regulus on not bringing Pandora to Elior Forest but he betrayed him and the village of elves. When Petelgeuse took in the Witch Factors of Sloth, Regulus mocked his incompatibility with the Witch Factors and expressed his disgust for his pitiful state, right before their battle began.
Lye Batenkaitos
Lye and Regulus assaulted Crusch's and Rem's caravan in Arc 3 interlude. While Regulus was stalling Rem and Crusch, Lye took care of the knights that were accompanying the caravan. They both expressed dislike for each other, as seen when Regulus scolded Lye's uncontrollable hunger, and the latter snapped back at him, saying "they hate lecturing and they don't care about Regulus' views and ideals". That being said, they weren't hostile towards each other, despite the well known fact of Sin Archbishops fighting amongst each other.
In the anime adaptation of the Arc 3, Interlude 2, Regulus even helped Lye take care of Rem quicker by incapacitating her, giving Lye a chance to eat her name and memories.
Sirius
Their relationship is extremely hostile. Regulus expressed deep disgust of her one-sided love towards Petelgeuse, even going as far as calling her worthless scum and a flawed being.
Natsuki Subaru
Subaru confronted him during his and Emilia's wedding in Priestella, which led to a battle that Reinhard joined in on and concluded with the death of Regulus. Regulus and Subaru started off on a rather respectful note, but they soon started to strongly resent each other; Subaru's dislike stemmed from Regulus' abduction of Emilia while Regulus found fault in Subaru's talkativeness and disregarding of his opinions which, for him, meant Subaru was belittling his rights, therefore he felt he should have been punished appropriately.
Emilia
Regulus and Emilia first met 100 years before Subaru's arrival, in the Elior Forest. Regulus would always remember her as that brat who's been crying and yelling nonstop when he went to retrieve his 79th wife.
After Fortuna's death, Regulus kept the 79th seat vacant for someone special. Upon laying eyes on Emilia in the Watergate City of Priestella, he set his mind on marrying her. At first, Emilia was very grateful for him saving her but soon she realized something was off. His way of speaking and his aura of death unsettled her. She soon made up her mind on saving his wives and defeating the Sin Archbishop. Regulus on the other hand thought quite fondly of her. Since she had a beautiful face, was pure, and was a virgin, she checked all the boxes for a "perfect wife". Soon after Subaru and Reinhard's arrival however, he realized she talks too much and decided on killing her. He realized her true identity and her connection with the events of Elior Forest moments before he hit the ground, setting his mind on killing her no matter what it takes. Sadly, it was too late for him, and he drowned with only one wish; that Emilia would not get any satisfaction from his death.
His first wife
Ever since he was a small boy, Regulus always had his eyes set on one village girl. Not much is known about her but Regulus seemed to think she had some feelings for him as she was the only one in the village who gave him attention. Once he obtained the Witch Factor of Greed, he slaughtered her family, broke her mind and forced her to marry him, thus becoming his first of many wives. It turned out she did not possess any particular feelings for him as she never laughed, let alone enriched his mundane and monotone life with a smile but due to Regulus' warped and distorted view on the world, he didn't think much of it; to him, all that mattered was her beautiful face which was the reason he married her in the first place. Somewhere down the line she died in an unexplained way, but right before dying, she laughed for the first time. Regulus didn't take that laugh all too well, swearing he'll never be alone anymore. On top of that, he forbid his future wives to show any facial emotions; a rule which would result in their deaths, if broken.
His wives
For well over 100 years, Regulus has been married 291 times. In order for his Lion's heart ability to work properly, he has been keeping them by his side all the time. He has been choosing his wives based on their faces. Accordingly, smiling, crying or any other form of facial expression that his wives weren't displaying at the time of their first encounter is strictly prohibited and will result in their deaths (a habit/rule he developed after his first wife's demise). Although he claims he loves them all equally, he will not hesitate to kill them if he feels like his rights were belittled or if he isn't satisfied with their face. Throughout the years, he has killed 238 wives, leaving only 53 alive. It is also worth noting that some of his wives were just as corrupt and scummy as him. Some killed people, some were Witch Cultists, some enjoyed torturing people and animals, and some were greedy. One wife even sold her younger brother for a new dress.
Regulus thinks love makes it so people are unable to be independent, so he decided on gathering a group of good-looking women who are virgins, as to not be betrayed and/or fall in love with them, resulting in him being independent.