NPCs listed in alphabetical order. Check all NPCs in your party, as I only list those that start the conflicts. For example, Edwin may have a conflict with Dynaheir, but it is Dynaheir who starts it, so Edwin is not listed for that. He is listed for the conflict he starts, though... The "Chance of attack" listed in parentheses is regarding the chances of a specific thread triggering, even after the unlikelyhood of a dialogue triggering at all, and then pointing to those two characters.
Also, this was done with the vanilla game. I cannot comment on any mods, like Tutu, that may change this. If you do have any mods, I'd look out for all of those listed (including the 0% ones) and more. (For example, I ran into an unfortunate and unresolvable conflict between Kivan and Montaron in my Tutu run with the BG1 NPC Project mod.)
-Ajantis: The worst of them all. He'll go after anyone that's evil, which includes Edwin, Eldoth, Kagain, Montaron, Shar-Teel, Tiax, Xzar and Viconia. (Chance of attack: 10%.) Fortunately, Ajantis does not become unselectable, so you can easily call him off by telling him to go somewhere else.
However, having Xan in the party can fend even this minor inconvenience off. Xan derides Ajantis every time he hears Ajantis make a speech about evil, and when he does that it keeps Ajantis from attacking. Just make sure Xan is near Ajantis at all times.
-Branwen: Has a problem with the "heretic" Tiax. (Chance of attack: 10%.)
This one is very very weird. It uses the variable from the Quayle-Tiax fight, so it will trigger that fight if Quayle is in the party and close enough for them to draw a bead on each other. otherwise, Tiax will turn unselectable for a moment and then turn right back. (If Quayle is in the party but is not close enough, he'll do the same.) You'll also notice that if Quayle is not in the party, Biff the Understudy will show up to deliver a line.
-Dynaheir: Has an obvious problem with Edwin. (Chance of attack: 100% certain.)
Having Minsc in the party decreases the chance to 50%. Having Alora in the party may bring something up, but it doesn't decrease the chances any, as that thread is weighted lower.
-Edwin: Joins your party to hunt down Dynaheir. You can get past this (100%) problem by picking up Dynaheir first. Edwin will then join you to keep an eye on her, and they WILL come to blows eventually. But you can have both Minsc and Edwin in your party without any trouble if Dynaheir is gone.
-Eldoth: Shar-Teel has a serious problem with his chauvinistic ways. (Chance of attack: 33%.)
-Jaheira: Has a problem with Xzar. (Chance of attack: 50%.)
-Khalid: Has problems with both Montaron and Xzar. (Chance of attack on either: 50%.)
-Kivan: Has a problem with Viconia. (Chance of attack: 0%.)
Kivan's attack on Viconia happens in a thread that is lowest-weighted and effectively screened out by the other four. I have not been able to produce it even with repeated testing.
-Quayle: has a problem with Tiax. (Chance of attack: 33%.)
-Shar-Teel: Still has a problem with Eldoth, even when he doesn't start it. (Chance of attack: 33%.)
-Tiax: Has a problem with Quayle. (Chance of attack: 5 or 16%?)
Goes through two validations. The first one is one in six, the second one is one in three. Either way, you're much more likely to get it from Quayle starting it.
Tiax also has a problem with Branwen. (Chance of attack: 0%.)
Thread hidden like Kivan's, and then continues on through Branwen's 10% validation. Also suffers from the bad variables, and so still would not result in a fight with Branwen, but perhaps with Quayle. Quite perplexing, and the height of pointless coding. O_o
-Viconia: Has a problem with Kivan. (Chance of attack: 0%.)
Hidden like Kivan's beef with her is.
-Yeslick: Has a problem with Kagain. (Chance of attack: 29%.)
In summary, the only ones you'll actually have trouble with are:
Ajantis vs. anyone evil (though you can call him off)
Dyanaheir vs. Edwin
Eldoth vs. Shar-Teel
Jaheira & Khalid vs. Montaron & Xzar (Jaheira & Montaron get on okay, though)
Kagain vs. Yeslick
Quayle vs. Tiax