I think there is a fine line between 'rude' and 'appropriate' in this case.
- Simply stopping to respond to requests without signaling in any way, that you are not interested in continuing the interaction is rude (aka ghosting).
- Signaling even just once that you would not like to continue the interaction (as clearly and polite as possible) and ignoring the other side from that point on is appropriate.
Even though you might not 'owe anyone' anything, humans typically have socially accepted behavior patterns. So the argument is less about what you must do and more about what the majority of people around you consider good style. However, these things might differ between cultures and social circles.