ESP8266 NodeMCU first WS2812 LED lights up green
So here comes my solution: I was playing around with NeoPixelBus by Makuna and the examples. I noticed in one of his examples, it said:

// You can also use one of these for Esp8266,
// each having their own restrictions
//
// These two are the same as above as the DMA method is the default
// NOTE: These will ignore the PIN and use GPI03 pin
//NeoPixelBus&lt;NeoGrbFeature, NeoEsp8266Dma800KbpsMethod&gt; strip(PixelCount, PixelPin);

So I tried outcommenting that line and used that instead, and then it worked! I've always used Neo800KbpsMethod whenever I saw NeoPixelBus being used, because that was what other people did. Notice it also said:

These will ignore the PIN and use GPI03 pin

That pin is the RX pin on my board. No other example I have seen, has used the RX pin on the board.
After 6+ hours of constant troubleshooting, I can finally power on my strip and control each LED!