Note- there are a lot of spoilers in this post.
From the beginning, Trip has shown he sees Kanto Trainers as lowly. He feels that Unovan trainers are greatly serperior (see what I did thar? haha). Defeating Ash's Pikachu, his starter, after Ash bragging so much about it only further boosted Trips opinions of Kanto trainers, as well as solidified Trips view of Ash (Ash = Not a good trainer).
Their battles throughout the series also furthered Trip's degrading of Ash. Ash didn't have 6 Pokemon yet, Ash only had 2 badges, Ash makes bad type decisions, as well as doesn't notice why his Oshawott can't aim. All of these things and more add to Trips opinion on Ash; Ash isn't good enough for Trip to battle. Trip's whole thing is to become the best, and he feels battling Ash will only allow himself to become complacent, thereby hindering his goal to become good enough to battle Alder.
So Trip doesn't hate Ash, he just has low opinions of him.
Georgia and Iris, on the other hand, isn't hate because of who they are (so much). It's what they are. Iris is an aspiring Dragon Master, while Georgia is a Dragon Buster. Georgia hates dragons, while Iris loves dragons. They contrast. Add in the fact that Georgia is very obnoxious and Iris is very condescending and you have a pair that'll go together as well as cats and dogs do.
Which is not very much.
And that brings us to the final rivalry; Cilan and Burgundy. Cilan has no animosity towards Burgundy; she's merely a trainer he once battled and an aspiring Pokemon Connoisseur . He only ever tries to out do her when she challenges him to a Pokemon Connoisseur battle. He easily outmatches her, and he does so unconsciously.
Burgundy hates Cilan because she's a very headstrong, prideful person. Cilan completely trounced her in her first Gym Battle, when she felt confident. She took that defeat very personally, and her perspective changed the way she saw things, turning Cilan into an evil person. So, in an act of her own self-righteousness, she vowed to beat Cilan. At everything.
So to answer your question, Trip doesn't hate Ash, Georgia and Iris hate each other because one's cat and one's mouse, and Burgundy hates Cilan because she's a sore loser.