Two of my players' characters had a large in game argument.
My Kitsune sorcerer insulted my Wayang bard a couple times. After the Wayang was called an “it” and compared to a goblin, this started a fight between them: she needed more respect, while his character didn't see that as being disrespectful.
Out-of-character the players are fine, but it took up a huge chunk of time in the session. At what point should I step in? How can I push them forward without just saying STFU and continue?
Stop them when it gets boring or nothing new is brought to the scene.
What you have is a role-play segment driven by your players. Congratulations for having players who will do this without a trigger from you and who can have an argument in-character without it spilling outside the game.
Here are the symptoms I usually keep an eye out to know if a role-play segment has run its course and should be pushed along. What I will say applies to most descriptive or role-play segment no matter who started them. Once you feel like the scene has run its course, it's your job to shake up the scene to make it interesting or let the scene fade to black to keep the pace of the real-life game.
The latter symptom is something I see a lot, as a player, in a currently running game. Another player and I love to play the two-incompetent-cop role, so situations where he leaves the scene to talk to an NPC or that we start bickering are relatively common. In those cases, after a little bit of banter, someone usually calls that "we keep on like this for a while, you can continue the scene". (And we chime in when we have new things to say.)
Its an interesting fact that some people who play table-top role-playing games get their fun from role-playing. An in-character argument over an insult is role-playing. If this is where your group gets their fun - you're doing it right.
Alternatively, if some members of your group found this dull, uninteresting and distracting from the fun they get from role-playing games (i.e. not just "not fun" but actively "unfun") then you should intervene and move on to something they find fun after the people who do find it fun have had a bit of fun with it. "They" could be "you", of course.
There is no definitive answer as it depends on the mood however i can propose several solutions to remedy this. I am listing my solutions from the most useful to least useful.
Talk to other players in private and learn their feelings before talking to the pair and telling them that everyone is a bit disturbed by how long they take.
Tell them that after five minutes for each minute they talk 10 minutes passes in game. This is a slightly extreme measure but it works really well when you need to hurry things along.
Ask the other players in front of those argue whether they are disturbed or not. Chances are they will agree with you. When they say they are disturbed then it will create a certain amount of pressure on the pair to not push it too hard and you won't seem like a jerk for telling them to hurry things along.
One thing I heard/read a long time ago is that extended in-game dialogue can be a source of noise or activity that would attract "wandering monsters". I'd hope a few of those would drive home the point of keeping things moving forward.
