If I have two distribution panels installed on the wall side by side. Let's say only 6" gap between them. The right one is calculated as category #4 and left one is calculated as category 0. How should I put the labels on panels? I am kind of heistate to put category 0 on one panel since it is so closed to the right one. What if the electrician wears PPE (categroy 0) to operator left panel but there is an arc fault started from the right panel? Maybe I am too conservative?

You need to label them for the AFH for the specific panel. Obviously, if someone is working on the higher hazard panel, then no one can be working on the lower AFH panel unless they have PPE on for the higher AFH panel. That is because they are most likely within the AFB for the higher AFH panel.

Label each according to its actual IE. I would not try to over anticipate. As a rule I feel most safety and design codes are conservative enough already without adding more. I hear all the time that these are 'minimum' codes. But I find most professional codes to be conservative as written.