#2012 slash

Raph is the first to find out about Karai's existence and the evidently one-sided "friendship" Leo has with her, but rather than immediately go on the offensive with Karai (extremely surprising considering she had Leo pinned to the roof right when he arrived) or accuse Leo of any wrongdoing, he simply demands an explanation from his brother. Raph observed the situation with a level head and didn't judge Leo for anything other than seeming too blasé about Karai being a Foot clan member, or for saying she wasn't intent on killing him when she threw a weapon at his head. Other than that, he kept the matter between him and Leo since it didn't seem to be a pressing issue at the moment. His trouble with Karai only really began in the next episode when he witnesses Leo needlessly showing off in front of her and even going out of his way to hide her from Splinter, Donnie, and Mikey.

Nothing's stopping Raph from telling everyone, and he certainly doesn't trust Karai enough to leave things as they are, but he puts his faith in Leo and nudges him to come clean about his new found friend twice to their brothers at least. Soon after being told that Karai was 'taken care of' (something he called total BS on), he reaches his boiling point once he discovers her following them, and his frustrations are worsened by Leo going out of his way to defend Karai when she's spelling trouble for them. As to be expected, Leo is forced to confess after she lands them in hot water and leaves them for dead while running off with a Kraang bot, but once Splinter gives him a much needed lecture, Raph forgives him and seemingly stays out of his face about the ordeal. At least until Karai approaches them with a proposition to combine their forces and fight the Kraang, something he surely would've put up more of a fight to shoot down had the others, namely Leo, not agreed to her offer after she helped them fight the Kraang stealth ship.

All of those instances, when combed through for the little things, are some of the first details the writers gave us to show a major distinction between Leo and Raph.

Raph's temper is so front and center throughout the series that the amount of patience he exercises in response to Leo's asinine decisions and trains of thought (especially early on) has a tendency of being overshadowed. He constantly, and openly, shunned the idea of Karai ever siding with them since he couldn't find it in himself to readily trust her like everyone else could, and even after learning who her real father is, he continued to question the possibility of Karai ever turning out to be good when considering her upbringing. But he still went along with Leo's wishes to help and go so far to befriend her because he knew his brother was simply trying to help someone out of the kindess of his heart at the end of the day, and Leo's only further spurred by her being their sister.

This isn't exclusive to their development with Karai, because we see later on that Raph exercised a far greater amount of that patience when Slash made his theatrical return to the team midway through S3.

One could make the argument that the writers should've had the midseason two parter focus the slightest bit more on Raph's POV since Slash used to be his pet and Leo was the only one unwilling to believe he'd changed since their last encounter, but I'd say with certainty that the minuscule amount of input we received from him is just the right amount of focus we needed. Raph doesn't blow up at Leo for his treatment of Slash because he knows his suspicions aren't baseless, and he doesn't go out of his way to prove Slash's innocence to Leo (Mikey kind of does that for him lol); he only decided to step in when the two couldn't decide on what plan to proceed with. He plainly moves aside and allows Slash to prove Leo wrong through his own efforts, all while undoubtedly believing since their last encounter that Slash isn't bad anymore and that Leo would eventually come around to make that same conclusion.

The complete opposite of Leo's stubborn behavior when it came to Karai.

Look at Leo's face, he's so silly, a goofy goober if you will

Even though she went on to turn her back on Shredder, and essentially prove that Leo was right, Raph wasn't wrong to take so much time to see Karai as a trustworthy ally. He recognized that it wasn't enough for her to just be borderline friendly and fight on the same side as them; legitimate effort needed to be put forth for them to warm up to someone like her, and her track record didn't exactly suggest that she'd readily put in that effort. Leo's fixation with turning the tables on Shredder and making things right with Splinter practically blinded him from that simple little truth though. Of course, he learned the error of his ways and clearly followed in Raph's footsteps when confronting Slash and anyone else they'd cross paths with that posed a potential threat, sometimes tending to go too deep into that mindset when he was upset with Fugitoid and Usagi.

The main leaders leading the resistance are Splinter, Karai, Bishop, Casey and Angel's dad, Slash and Newtralizer. Newt originally wasn't apart of the lead, but the others noticed his knowledge and him being able to navigate thru Triceraton tech and even knowing some of their weaknesses. Surprised by this, they offer him a position in the resistance. Newt was rather hesitant,and he felt upset he showed his knowledge too much than he should have. But that hesitance quickly died out because he didn't want yet another alien invasion so he immediately joined.