After messing around a bit, I finally found out how to remove the webcam background in OBS Studio. Here is my quick guide how to do it.
- Open OBS Studio
- Right click on your webcam feed after adding that as a source into a scene
- Select filters
- Press + on "effect filters" to add a new filter
- Select "chroma key"
- Adjust similarity and colors until you got what you want
- Done!
You should use a greenscreen or something behind you for best results.