Hi guys.

I know that 行く can be pronounced either "いく" or "ゆく”.

Something that I find interesting is that often when it's written in te-form as
"ーていく"　people still pronounce it as ”ーてゆく”, even though 行く is written as いく。

So basically, people are pronouncing い as if it were ゆ。
This seems fairly consistent when I hear it in karaoke.

One example is 0:52 into this song:

No just this song, but many other songs that use ーていく.
So I don't think it's a slip of the tongue (no one seems to correct themselves and say "-te iku").

I just find it a bit strange because Japanese natives are changing the pronunciation of a hiragana character. Or are supposed to make an exception and treat い as a kanji character (with 2 pronunciations: "い" and "ゆ") in this instance?

行く is written as 行く and pronounced as either いく or ゆく.

ゆく has a more poetic feel to it so you hear it often in songs. This is correct and in no way are people "mispronouncing" anything when they do it.

Edit: sorry I misread what you wrote. The ていく in karaoke script but with a singer singing ゆく is probably a typo.

Note that ゆく is a much more older reading than いく. In classical Japanese, at least until the Heian period it's always ゆく.