Many advices say RAW files are not affected by picture control.
However, when shooting, LCD shows preview according to picture control selected.
The "many advices" are precisely correct, so I think you maybe are not getting the meaning. The raw data in the raw file is Not affected by the camera settings (other than exposure). However, raw files also include an embedded JPG file which is affected by the camera settings. This JPG data is used to show the rear LCD preview and the histogram (which raw cannot show), but the raw data is not affected by it. The raw file is only affected by whatever settings you apply later in the raw editor. This makes them be rather different pictures, controlled in very different ways.
One complication about understanding this is if you might be use a simplest photo editor (like Irfanview or Faststone), these will OPEN raw files, but they are NOT raw editors, and they ignore the raw data and simply use the JPG data, which just means you wasted the effort and bytes of selecting to shoot in raw. That offers NONE of the many advantages of raw, so if you want to shoot JPG, then just shoot JPG.