Archer: This happens a lot; the ISIS employees tend to get into petty fights on a daily basis. Whenever Archer and Lana are on mission together, Archer tends do stupid things that mess up their mission. Things get worse when the rest of ISIS take part in a mission, at least one of them will slip up, or were the cause of why their mission is compromised.
Carmen Sandiego: Tigress and Paper Star have a hatred for each other despite them both being in VILE as shown in the epusode "The Haunted Bayou Caper" even to the point of being completely uncoordinated in combat with Carmen Sandiego herself.
Castlevania (2017): Trevor's abrasive personality makes it difficult for anyone to co-operate with him. When he rescues Sypha from petrification in the castle dungeons and she stays with him to find the Sleeping Soldier, she still considers him to be rude and considers the merit of making him drink her urine. It's even worse when they join up with Alucard, who, being a Dhampyr, naturally has reservations about working with a Vampire Hunter like Trevor. With that said, though Alucard and Trevor frequently trade barbs and threats with one another, they still sometimes make one another laugh.
Code Lyoko: The Five-Man Band starts out like this, evolving into True Companions as the series goes on. Though technically fueled by their Power of Friendship towards Aelita, in the beginning they don't really have much loyalty to each other, and it's kind of easy to get them to break up or lose at least one member.
Iron Man: The Season 2 opener ends with Force Works dissolving as Scarlet Witch, Hawkeye, and Century decide to quit after Tony fakes his death and War Machine and the Julia Carpenter Spider-Woman deciding to stay. While Spider-Woman, Century, and Scarlet Witch don't hold anything against each other, War Machine and Hawkeye do have contempt for the other's respective side, with the latter being an ass to Rhodey and Julia for staying with Tony, and Rhodey likewise being hostile towards Clint and even making a snide remark about Wanda in regards to their leaving after she and Clint return (Century, at least on-screen, escapes Rhodey making snide remarks about him).
Kim Possible has this happen occasionally, notably in the episode "Go Team Go" when Shego teams up with Kim and her estranged family to defeat Aviarius.
My Little Pony: Friendship Is Magic: In "To Where andBack Again", the sixth-season finale, a team of misfits assembles to do the world-saving typically done by the protagonists, who are indisposed. Although the group members are not all averse to teamwork, none of them are used to being team players, and at least one is actively antisocial. Of course, this just makes the group dynamics all the more interesting, and the eventual victory all the more fulfilling.
Rick and Morty: In "The Ricks must be Crazy", Rick and Morty encounter Zeep, an inhabitant of the micro-verse Rick created to power his car. When Rick demands to know why the micro-verse isn't generating electricity anymore, Zeep reveals that he created a mini-verse to power his world, where they discover that an inhabitant of the mini-verse intends to do the same thing in a teeny-verse he's just created. After being stranded for months inside the teeny-universe, Zeep and Rick spent that time arguing over who's smarter. When Morty shows up leading the Tree-People, he tells Zeep and Rick to work together and fix the machine that will transport them home, just as they are going to explain why they can't work with someone whose intelligence they consider inferior, Morty sics the Tree People on them. Sometime later, they fix the machine, they exit the teeny-verse, and their rivalry resumes.
In Jack in the Scotsman's relationship starts out this way, with them (despite Jack's best efforts) getting into a prolonged fight almost immediately after meeting each other and only end of (reluctantly) working together, because a group of bounty hunter handcuffed them together. Though after they get themselves out of that predicament, they have grown to respect each other as warriors, with the Scotsman even becoming Jack's only real recurring ally for the first four seasons, with them still occasionally butting-heads, but more as a friendly rivalry, than genuine displeasure with the other.
There's also a villainous example with Josephine and Ezekiel Clench, a pair of formerly married bounty hunters, who reluctantly put their differences aside to capture Jack, but spend just as much time bickering with each other. They actually do manage to capture Jack, but Josephine lets her greed get the better of her and betrays her former husband, giving Jack the opportunity to free himself.
When Ahsoka crash-lands on Level 1313 of the Coruscant underworld, she quickly befriends Trace Martez, but her older sister Rafa is a cynic who has developed a mentality of not trusting anyone who isn't family. In "Dangerous Debt", when the trio are trying to escape from the Pyke Syndicate, this leads to, among other things, Rafa attempting to persuade Trace to ditch Ahsoka when it looks like she's trapped on the other side of a retractable bridge (not a problem for her); and when Rafa suggests that Ahsoka go to open the gate while the sisters distract the guards, Ahsoka snarks that that must mean Rafa thinks that task will be more difficult.
The Bad Batch tends to have this when they work with regular clone troopers (or, specifically, Wrecker and Crosshair have this attitude). In their self-titled episode, Wrecker actually chokes Jesse during a disagreement over who's going to be in command of the operation since Commander Cody is too injured to carry on.
Star Wars Rebels leans heavily on this trope to drive character development. In particular, Zeb and Ezra cannot stand each other and fight continually. Nevertheless, they begrudgingly respect each other's capabilities and, of course, dedication to their common cause.
Teen Titans: Slade teamed up with the Titans to save Raven and the world in the "The End" episode arc. Slade and the Titans still absolutely hated each other's guts, but managed to cooperate for some time. (Craziest part? Slade was at least trying to be polite about it, Robin was not.)
Starscream and Megatron are stuck working together for good part of season 3. They clearly hate each other and don't even bother to hide their contempt for the arrangement.
Lugnut and Shockwave are united in one thing and one thing only; Undying Loyalty to Megatron. Otherwise they absolutely despise each other and spend most of their time fighting to prove whos the better underling, whilst an increasingly annoyed Megatron wants them to just shut up and do their jobs.
The villains Sportsmaster and Cheshire obviously can't stand each other from their first appearance together. Fridge Brilliance kicks in a few episodes later when it is confirmed that Sportsmaster is Cheshire's (verbally and emotionally abusive) father, who she ran away from home to escape.
This also occurs between Kid Flash and Artemis for a while after Artemis' arrival, since Wally saw her as usurping the position that should have been occupied by his friend Spee- sorry, Red Arrow. All of this ends when they enter a relationship in season 2.