Our first was a team of an Enchanter (specialist mage), who would be joined early on by Imoen, the NPC thief who joins your party a short time into the game. They also chose "Find Familiar" as one of their level 1 mage spells, enabling us to be joined by a powerful pacifist run ally of a Faery Dragon familiar capable of casting a very advanced invisibility spell, giving them a huge initial advantage.
The second was G.W. Trevelyan's halfling thief McGibbits, whose run was originally planned as a solo thief campaign in which he'd attempt to solve all the quests alone (and therefore acquire all the xp points for his own use). However, McGibbits ended up changing his mind since many of the best pacifist run quests were only solvable using a combination of a Charm spell (an Enchantment spell) + the thief's pickpocketing abilities (since it's impossible to pickpocket hostile creatures).
So in the end, both groups of players ended up using a team of a Thief + Enchanter, making heavy use of the Stealth, pickpocketing, and lock picking skills of the thief, and the Charm Person and Invisibility spells of the Enchanters. (This enabled us to get almost all the way through the game, with the caveat that you'll eventually have no choice but to recruit a significantly tougher group of adventurers near the end, if you intend to take on the last boss without using cheats codes.)
A note on XP and leveling up your characters without fighting:
Baldur's Gate follows the D&D tradition of making you divide any yield of experience points evenly between any characters on your team at the time the xp is awarded. This + the pacifist challenge restriction against fighting in order to gain xp means that experience points are also quite scarce, coming mainly from solving nonviolent quests, so ideally the xp should be directed only at your most important characters.
However, it's usually also possible to bring along more allies most of the time, and then politely request that they leave the party temporarily so that only specific characters receive xp rewards.
(One last technical note: We used various custom portraits in our games for fun, but for those who might want to pick up the same NPC characters: The NPC thief seen in screenshots of group 1 was Imoen accompanying the PC enchanter, and the NPC Enchanter with group 2 accompanying the PC thief was Xan.)
A hallmark of Dungeons & Dragons RPGs is that players get to generate their own player characters to take on their adventures, and a player's choice of starting character for a pacifist run through Baldur's Gate is going to make a huge difference to how smoothly the campaign goes.
You can be one of a number of fantasy races, including Elves, Halflings, Humans, Dwarves, Gnomes, or Half-Orcs. Most have some type of special abilities and bonuses that make them better in some classes and worse in others. In our case, the races of interest were Elves (because they get magic, dexterity and stealth bonuses, among others) and Halflings (who get the best thief-skill and stealth bonuses).
The choice of "class" has a huge impact on what actual skills and abilities the player will end up with. For example, only thieves can use the pickpocketing skill, and only mages or clerics can cast many of the spells available only to their own class. (There are often treasures, potions, wands, and scrolls that create some overlap, but some of these are only usable to certain classes, making it difficult to predict what will/won't be available, or which ones will work.)
Players can choose whether to be fighters, mages (generalists, or specialists in one of many magical disciplines), thieves (later renamed "rogues", since they can be used with or without stealing anything), rangers, or clerics. There are also sub-classes of each of the above, such as druids (a cleric/priest subclass) who can charm animals and use nature magic.
The attributes (strength, intelligence, dexterity, and so on) one rolls and allocates will have a major role in determining how effectively each class uses its skills, but the fundamental abilities of each class are even more important.
BEST PACIFIST RUN CLASSES
There might be a lot of viable pacifist run strategies out there we never even thought of, but our top choices were the Mage (specifically the specialist mage, "The Enchanter") and the Thief. The Cleric also has solid potential.
You will never actually be forced to steal anything in Baldur's Gate even if you play as a thief, but thieves are still extremely useful classes to use in a pacifist run through Baldur's Gate I. Even if a "thief" character never steals anything (even from villains), the thief class excels at "stealth" skills that enable them to conceal themselves in shadows to avoid confrontations with enemies. This ability can also be used repeatedly (after a short cool down period after failure), unlike mages' spells that can only be cast as many times as their level allows after memorization. The ability to enter and leave the shadows repeatedly makes a huge difference in many cases while sneaking through hostile enemy-infested strongholds or wilderness areas, since simple actions like opening locks or chests will break the invisibility condition in most versions of Baldur's Gate.
Depending on how you allocate skill points, the thief's skills can also enable them to open locks, pick pockets (which is sometimes important to steal key quest items from villains without resorting to violence), and do several other useful things like detect traps.
If you're using a thief as your main character in a pacifist run, you will probably want to maximize stealth skills as soon as possible. (This will require some "legwork" to complete nonviolent quests while running away from enemies after low-level stealth skills fail, but that is often a lot of fun in its own right. Once your thief has passable stealth skills, a thief-oriented pacifist run starts to go even more smoothly.)
The only significant weakness of a thief is that they lack the ability to use magic, and in particular the "charm" spell, which is why thieves are even better when teamed up with magic users...
MAGES AND SPECIALIST MAGES
Three indispensable abilities during a pacifist run through BGEE are the ability to conceal one's self from enemies, to cast "Charm" to turn hostile foes friendly temporarily, and also to open locked doors and treasure chests. A mage with enough xp can theoretically do all three of these things, arguably making them the single best choice for a solo pacifist run, and a highly valuable asset for a run with some NPC allies.
Invisibility spells are available for purchase and can be learned after a few level gains, Charm is a level 1 "enchantment" spell from the very start (and works even better for Enchanters, since the spell comes from their specialist discipline of magic), and mages can acquire a lock-opening spell called "Knock" later in the game.
The only thing I know of that a mage can't do by themselves is to pick hostile foes pockets (or anyone elses' pockets for that matter), a skill which is not 100% vital, but is extremely useful for quite a few quests where one wants to nonviolently reclaim stolen items.
The big advantage the mage has over the Thief is that their invisibility spell is not only long-lasting (24 in-game hours, if we remember rightly), but it also works regardless of surrounding conditions, whereas a thief's stealth skill can only make them invisible to hostile foes with a combination of high skill and satisfactorily dark or shadowy conditions.
Even the best stealth assets have their limitations, though, since the invisibility and stealth effects are cancelled when the character picks up objects or treasure, open doors and locks, or tries to talk to another character in the game....
COMPARING STEALTH SKILLS OF THIEVES AND MAGES
The Thief's stealth skills have both advantages and disadvantages compared with the mage's ability to cast invisibility:
Stealth skills require a combination of either higher skill levels and/or sufficiently dark conditions to take effect, but even when they fail temporarily (e.g. if Hide in Shadows fails after stepping into a brighter patch of torchlight), they can be re-tried over and over again after running away just enough to get out of pursuing foes' line of sight. This is very useful (as well as fun and humorous) when grabbing foes' treasures, and then running away to re-conceal one's self in the shadows.
A wizard's invisibility spell, on the other hand, can only be re-cast a few times until the wizard reaches a high level, which can take a long time in a pacifist run where nonviolent xp is scarce.
Its advantages are that it lasts a very long time, it will work even in the brightest conditions, and most importantly: It can be cast while the mage is directly in enemies' line of sight, as long as the mage doesn't get hit with an attack that causes the casting to fail (which can easily happen if one is not careful).
Clerics, priests, priestesses, druids, and related classes usually combine warrior characteristics with their own special sets of spells, which vary depending on their patron deity.
Clerics would be a favorite class in a "normal" run through the game, and some players also choose them for a pacifist run since even level 1 clerics get a spell called Sanctuary that conceals their presence from enemies in a similar way to a thief's stealth skill and/or a mage's invisibility spell (though we personally found the latter two assets preferable).
Our impression was that the "Sanctuary" spell took longer to cast than the mage's spells, and also had shorter duration, but with the advantage of being available from level 1 at the very start of the game. However, there are plenty of nonviolent quests to complete to level a thief and/or mage up enough to get solid stealth and the invisibility spell even during the early part of the game.
If you didn't mind splitting experience points three ways, on the other hand, a Cleric might make a great addition.