Stamping passport while travelling

It depends on nationality. All non-European passports will be stamped EU entry and exit controls. No matter if you have residence permit or not. The passport may be stamped as well in your non EU destination country. In EU its just all the European passports which will not be stamped considering the right of freedom movement.

Aha, the exception indeed is F card holders, that is an article 10/20 card so it confers on the holder the possibility of freedom of movement like an EU national in the EU/EEA/Swiss area.

If someone wants to specifically NOT take up their freedom of movement rights under EU Regs 2016, then they can ask for their passport in these circumstances to be stamped, but usually you would not get your passport stamped if presented also a Belgian F card.

Had you given that infor in the original post, you would have gotten hopefully that answer from someone who is aware of EU Regs 2016.

Stamping passports for non-EU permanent residents of any of Schengen countries usually is not required. E.g. my passport (I am F card holder as well) was never stamped when crossing border in Belgian airports, the same thing is in Poland and Germany. Though every time I cross border in Vienna airport, it depends on the border guard: sometimes it is stamped, sometimes is not...