Is severing negative communication with an "incompatible" person a big no-no in the Buddhist pracice?
The Pali suttas say (Snp 1.10; SN 10.12) there are four qualities for the household life (which are also to be applied to any significant relationship), namely: 


Sacca (truthfulness; honesty; straightforwardness; openness; no secrets) 
Dama (training in self-improvement); and Dhamma (principles) 
Khanti (patience; forbearance; tolerance) 
Caga (sacrifice; generosity) 


Therefore, in a significant relationship, a person should truthfully communicate to the other person any concerns they have about their behaviour and both should train in self-improvement to abolish that unwholesome behaviour. 

If the other person does not respond and the relationship is toxic or harmful (intolerable) then cutting ties is OK. For example, one sutta says a wife (SN 37.30) without ethics is expelled from the household.