The importance of calm, reasoned discussion of disagreements cannot be overstated. If the objective is to find the right answer, or even an acceptable answer, then a polite and respectful exchange of views is likely to be the best way to proceed.
In the past week I have encountered two ways of preventing discussion. One was to declare a topic so sensitive that even a polite discussion had to be terminated for fear of giving offence. The other was to shout so loudly and be so abusive that reply was impossible, even if the person who disagreed was not intimidated by the aggressive display.
The way I see it, we either have to go on living together after our disagreements or erect permanent walls of hostility to keep out those we call 'them'. Banning discussion or howling down those of a contrary view are both ways of ensuring that disagreement will be followed by ill-feeling. Resentment is likely to simmer away; everybody is convinced that they would have been proved right if only talks had continued and nobody's understanding is improved in any way.
Both methods of suppressing discussion are ultimately self-defeating. Not only can you not win a discussion that you do not allow to take place, you are, more importantly, prevented from coming closer to your neighbour, understanding his point of view and making allowances for things that are of little importance to you and of great importance to him.
Even when points of view seem irreconcilable, it is important not to stop talking. Retreating into an entrenched and isolated hostility to contrary views is the way to conflict born out of enduring ignorance.