The tiefling has Fire Resistance and Hellish rebuke, which both have to do with fire damage. If I were to replace that with Cold damage, Slashing damage, Necrotic damage, Radiant damage, Psychic damage or any other damage type (assuming it made sense narratively), would it break or mess up the balance of the game in any significant way?
[RPG] Would changing the damage type on a tiefling’s abilities affect the game too drastically
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Best Answer
It depends on your campaign
The strength of any kind of damage depends on the campaign. While Sparksbet mentions the resistances from Monster Manual in this question - it matters a lot less than it seems. You are not using every monster in the Monster Manual. You are not even randomly picking monsters from the monster manual using an uniform distribution (I mean, you could be, but those would be two amazingly awkward, but possibly funny, campaigns). So, ultimately, it depends on your campaign.
If your campaign contains many monsters that are weak to fire, then yeah, changing it to anything else makes the Hellish Rebuke weaker. If you are in a campaign where the party is fighting red dragons and fire elementals, yeah, you would be doing a favor to the PC changing the damage type.
While András answer there does an amazing job, you are also (probably) not playing from 1 to 20. Again, what type of damage is most resisted/immuned also depends on the level range, which is also part of the campaign. For example, in Tier 1 (levels 1-4), monsters with immunity to physical (Slashing/Piercing and Bludgeoning) nonmagical damage are rarer, because otherwise martial fighters (Fighters, Barbarians, etc.) would suck too much without having magic weapons - which they don't early. On the other hand, in later levels, almost every monster has immunity to nonmagical physical damage.
So, while my answer might seem unhelpful, that's all we can correctly provide without more information about the actual campaign.
Finally, I will agree with Sparksbet conclusion: Ultimately, honestly, this change is not what is going to make Tieflings unbalanced (for better or worse). Giving them wings will :P (this is a joke, don't punch me please).
Note on Physical Damages
Giving resistance to physical damage is usually a no-no. You mentioned "Slashing" as a possibility - resistance to slashing would be way stronger than magical resistances. Evey creature has some attack that deals physical damage - even the highest CRs - and resistance to even magical slashing (or piercing, or bludgeoning) damage would be way stronger than anything else. Quoting the DMG in the Creating a Monster section, as an example of how "especial" these damage types are.