Icons crossed by horizontal white lines

My friend's Macbook Air (latest High Sierra) suffers from icons crossed by white lines. It's like couple of lines of pixels missing completely or moved one pixel up.

The Wifi icon in the menu bar shows this glitch when it's alone, but draws properly when we select it. The clearest images go this are finder sidebar icons (AirDrop, Documents etc) and menu bar icons (wifi, battery etc).

Some things to note:

1. We installed vanilla High Sierra and it still shows up.
2. Booted to Recovery Mode everything looks fine.

What might cause this so we can fix it or simply know the cause?

This is absolutely sounding like a graphics card issue (VRAM failure or part of the accelerated graphics pipelines have failed within the GPU itself). My thinking is that when you boot to recovery or safe mode, the graphics driver is operated in a very slow and limited manner (likely deactivating shader and vector processing optimizations, etc...). When that cures glitches you’ve got a very few things to consider now.

You've already installed a totally new copy of the OS so unless you didn't apply all updates to that OS - you've brought the latest drivers, no corrupt apps or add-on or user settings and proved the current OS and hardware fail to work. Excellent triage there to be sure it’s not software corruption or a preference issue.

Since Apple repairs MacBook by swapping in a new logic board - you would expect a $300 flat rate repair to fix this out of warranty but get a quote from them to be sure. Before spending money to fix, I'd probably be sure a safe mode boot confirms it's GPU related and be sure you have a good backup.

I dismiss it being the LCD or the connecting cable (but it could be either as well - even just the connecting cables are loose) since most of the time, that would cause lines no matter what was drawn and your WiFi icon curing itself on screen when the image changes makes me think the computer is generating the wrong image and the wrong image is being faithfully displayed as opposed to a good image from the GPU being corrupted by the cables and/or display.

Short term, you could increase the size of the elements to minimize the pain to see things or try using an external screen when you can.