Is it unbalanced to allow a player to move the tiefling's +1 Int bonus to a different ability score?

Question

I'm in the planning phases of a campaign for D&D 5e, but using the Planescape setting. Since this setting is the one which introduced tieflings, I sent the table of potential tiefling traits to my players, and told them that they could replace the tiefling spells/traits with something from that table if they wanted to.

One of them asked if they could change the +1 bonus to Intelligence score that tieflings get by default to be a +1 to a different ability score for their character (I'm assuming Wisdom, since I think they're playing a cleric), and I opted to allow it, so long as they didn't put it in Charisma.¹

I am the first to admit that numbers and overall game balance are not my strong points, and while I doubt that this modification is likely to be game-breakingly powerful, it's also extremely possible that I've misunderstood some numerical advantage that I've given this player. I also approved this change with the vague idea that one or both of the tieflings in the group might swap their racial spells for the ones given in the table, but I don't believe either of them is doing so.²

Does allowing a player to move their +1 Intelligence score bonus as granted to their race to another mental stat create a balance issue?

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¹ In case anyone wanted to know why I allowed this, I already have a (fairly well-earned) reputation with my friends for being the meanest/strictest of our DMs; I try to give lenience when I can. This is a group that leans more Adventure Zone than Critical Role with the rules, which is to say that the rules are frequently thrown directly out the window.

² Yes, two tieflings. So far, out of four players that have been in contact, we've got two tieflings, one half-elf, and one dhampir.

Answer 1

This is exactly what is suggested in Tasha's Cauldron of Everything

In the section "Customizing Your Origin" (TCoE, p. 7), there is a subsection on Ability Score Increases:

If you’d like your character to follow their own path, you may ignore your Ability Score Increase trait and assign ability score increases tailored to your character. Here’s how to do it: take any ability score increase you gain in your race or subrace and apply it to an ability score of your choice. If you gain more than one increase, you can’t apply those increases to the same ability score, and you can’t increase a score above 20.

For example, if the Ability Score Increase trait of your race or subrace increases your Constitution by 2 and your Wisdom by 1, you could instead increase your Intelligence by 2 and your Charisma by 1.

So what you suggest should be fine. The effect of possibly being marginally better at a different saving throw will be barely noticeable. Every once in a while, they will succeed a save they will have otherwise failed, but they may occasionally fail a save they would have otherwise succeeded.

There are tiefling subraces that do this already.

In addition to the optional rule quoted above, Mordenkainen’s Tome of Foes includes several varieties of tiefling that have different +1 ASIs, so there is already a tiefling subrace out there for you (the racial traits and spells will be different the base tiefling). Basically, Wizards of the Coast really wants you to play a tiefling with whichever +1 ASI you like.

I've been doing this since before the release of Tasha's Cauldron of Everything

The optional rule from Tasha's was nothing new to me when it came out. I have always been pretty permissive with my players about rearranging the racial ASIs, and I have never thought to myself "I wish I hadn't let them move their +1 around". The overall effect is much too small to unbalance anything, and it just helps players be more satisfied with the results of the character creation process.