MacBook Pro display suddenly has a very faint warm/pink tint

Old answer, provided as background

I handed in my computer with the problem to an authorized service partner. At first they didn't recognize the error, but after some further convincing from my part they claim to have spoken with Apple about it.

The authorized service partner claimed that the problem with warm hue is a software bug introduced in one of most recent versions of MacOS High Sierra (spring 2018), and it afflicts various Mac models. They claim that Apple is aware of the problem, and a fix will applied in an upcoming MacOS patch.

Edit, May 2021

As of MacOS Big Sur 11.2.3 (2021-05-04), Apple haven't applied a fix, as the problem persists.

Upon multiple further contacts with Apple, it has become clear that Apple's support are not aware of this issue. They have asked for video evidence when the issue occurs. I would encourage users who experience this issue to contact Apple and send video evidence to get the issue noted.

Since Apple isn't recognizing this issue, I have unmarked my answer as a solution.

It sounds like you have Night Shift on. It tints all of your screens colors to be easier on the eyes.

System Preferences > Displays > Night Shift > Schedule > Off

Try that and see what happens. If that's it, you might want to turn it back on and set a schedule that works better for you.