Agreed. The AL rules clearly indicate that the party applies to everyone at the table.... Otherwise, parties that split and go different directions would not pool treasure, and rogues who decide to pickpocket would be able to keep what they got.
All major rewards (XP, Treasure, etc) are split EVENLY between the party (with the exception of magic items, which are specifically divided according to the methods in the ALPG and ALDMG). It doesn't matter how a character contributes to an encounter, or even if the character was present for a given encounter - all rewards are totalled, and divided.
As the OP said themselves - the character participates extensively in the social (and from what I can tell, the exploration) pillars. Are you saying they are not entitled to XP simply because they have a preference for one pillar over the others (and in fact, have a preference for a pillar that rarely if ever awards XP by itself, unless a potential combat encounter is involved and overcome in non-violent ways).
Speaking of which, perhaps the party should engage in overcoming some combat encounters using non-violent (peaceful) methods. You still earn XP (providing you do something meaningful to overcome the encounter - a single dice roll doesn't cut it).
It sounds to me that there is a disconnect between playstyles... This player appears to prefer social/exploration while the rest of the party are combat-heavy and prefer a murder-hobo style. It is the DMs responsibility to acknowledge all playstyles, and find a way to balance them at the table. This means that they should not only encourage the player to engage meaningfully in combat (even if that means the character takes up a defensive position in a tactically strategic point and takes the dodge action....acting as a living wall and shielding the party from damage; or distract an enemy by taking the help action to grant a major DPR character advantage on their attack roll), but they should also encourage the other players to come up with nonviolent solutions on occasion as well.
There are plenty of ways a peaceful character can perform meaningful nonviolent actions in combat (I have already mentioned Help and Dodge, but there are also spells such as counterspell, hypnotic pattern, grease, wall of stone/force; the protection style, cutting words, the lucky feat, splitting the enemy by drawing attention and then hiding and playing peek-a-bco to keep them distracted; etc).
Its not about conformity - it is about blending.
I have a wizard who rarely makes attack rolls outside of cantrips. He isn't non-violent, he is just a controller and proactively reduces enemy effectiveness in combat. I think of him as a reverse cleric - proactively preventing damage (rather than reactively healing it). Sure, he will swing with his cantrips if he has nothing better to do, but he rarely casts damaging spells (preferring instead to cast things like polymorph, wall of force, and his two favorite spells - counterspell and hypnotic pattern). Polymorph works in two ways, adding a HP buffer to a key combatant (either myself or another character, whoever needs it most), and also improving DPR (giant ape anyone). The character compliments his style by being a front-line combatant, wearing half-plate (and carrying a +2 shield; for an AC of 21); and having the Lucky feat, mirror image and shield
as backups.
This character seeks to direct as many attacks at himself as possible (in order to spread damage around the entire party, otherwise HD are being wasted on short rests) and also for the purposes of negating those attacks via high AC, Lucky, mirror image and/or shield.
I haven't cast fireball, scorching ray, or a variety of other attack spells in months (doesn't help that we have been fighting a lot of fire giants though). In fact, to my memory - the only damaging spells I have cast in the last 2 months have been otiluke's freezing sphere (once), prismatic spray (once), animate objects (several times), bigby's hand (several times) and polymorph (frequently, when I am not otherwise using Hypnotic pattern orwall of force).