I think the main issue for a person who is different from the "Western moral norm", is to come to terms with who they really are, who they want to be, and then to accept themselves. Anyone that is different will have the snares of society to dodge, but once you have found yourself and is comfortable in your own skin, you can actually change other people's perceptions of you. Not if you whine and nag and moan and cry and have the oh-woe-is-me attitude.
Perhaps the intolerance and irritation of others (i hesitate to call them "normal") are created during the process of someone trying to become one with their own sexuality, their own moral belief system, their own spirituality. That process often creates havoc, and in a public space where such a person is searching, the havoc and uncertainty they experience spill over to the others involve, who do not want to be part of that process, and often can be callous.
Its such a sad world we live in where dislike can turn to hate, and intolerance can break an already fragile peace.
"Integrity" and "integer" both contain a Latin root meaning "whole; complete." The root sense, then, is that people may be said to be acting with integrity when their beliefs, words, and actions have a sense of unity or wholeness.