You don’t have the luxury of tuning anything out. You have to hear everything, process it, no matter how crazy and unreasonable and insulting it is.
You have to respond calmly and reasonably to these things. You cannot act insulted, you cannot act with indignation. You must seek the reasonable and fair conclusion to any conflict. You must first accommodate, then discipline.
And, most important of all, you must eat big shit sandwiches.