I think there is a lot of human nature buried here, and it occasionally comes to the surface with ugly results.
Human have historically been religious; atheism or agnosticism are relatively new; at least in public. And religions have historically been in opposition to each other. At relatively few times in history have religions been able to live at peace with those of other faiths. The majority tends to persecute the minority; borders create areas of conflict; state and religious goals and power struggles coincide, overlap, and compete with each other at various times and places.
Add to that the very human tendency to see any group which one is not a member of as a monolithic whole. Christians, while understanding that all Christians are not alike, tend to see all Muslims or Jews as the same. Those groups do likewise to Christians. Nations do it to each other. As different as individual Americans are, we tend to see all Germans as believing the same things or acting the same way; as they tend to do us. We understand the innate differences in our own group because we cannot avoid seeing it; we tend to presume that other groups are indeed 'the other' and therefore not possessing the same complexity, differences, and variations as we do. We can tell you what 'those Democrats believe' while accepting that not all Republicans believe the same things; and vice-versa.
Another human tendency is to attempt to place people into categories and assign them values that reflect our own prejudices about those categories. If a person defines themselves as 'conservative', then they are anti-abortion. If they say they are 'liberal', then they are for national socialized health care. In truth, we all know that our own political and religious beliefs tend to be unique, individual, and both grossly and subtly different from those of the party or religion to which we belong. We understand that about ourselves; we tend not to believe it about others. "We" are subtle. "They" are a stereotype we have created for them to belong to.
I suspect that we do this because it makes the world easier to comprehend. Things are the way they are because people behave in predictable ways, according to the gross set of beliefs to which we want them to adhere. Our economy is going to hell because we have a Democrat President, and he hates free enterprise and wants to socialize everything. Our economy is going to hell because we have a Republican President, and he loves war and wants to destroy cherished liberal freedoms. This is far easier to believe for many of us than the truths, which may be complex or even unknowable.
In the end, any definition to attempt us to understand groups qua groups is bound to fail. What do Catholics believe? What do Muslims believe? What do Christians believe? What do Republicans believe? The answers can only be given is the most basic, simple, and unsatisfying manner; unless one has a predisposition towards or against a given group anyway. If we're Christian, we tend to general statements about Muslims that fit with our world-view. If we're Muslims, it's the same about Christians.
In addition, we have the media added to this stew. The media does not make friends or sell advertising by pointing out to the people who like reading, listening, or watching them the many ways in which they are wrong, the many ways in which they fail to make distinctions between groups of people or jump to the wrong conclusions. A news group that has an audience comprised mainly of a group that distrusts Muslims, for example, won't be pleasantly regarded if they insist on noting the distinctions between various Muslim groups, or between those who favor militant action and those who do not. A news group whose audience is comprised mainly of those who distrust large corporations is not going to find favor with that audience by pointing out good news relating to deregulation.
Then we have political correctness. This is a relatively new phenomena. This is the force that drives some parts of modern societies to be 'progressive' and attempt to see beyond the basic labels and assumptions. It can be a force for good; changing the way we think and behave towards each other regarding such things as physical and mental disabilities, minority religions and others seen as oppressed or marginalized in society. It can also be a force for ill, when it gets out of control, imposing serious penalties for petty offenses or terrorizing citizens to eschew uses of words, phrases, or ways of thinking that are a set of moving goals, as well as being arbitrary based on the current zeitgeist. One is 'handicapped,' then 'disabled', then 'differently-abled', which distorts the language in a well-meant attempt to not show a person with a physical infirmity as 'less than', but becoming so shrill, militant, and at times, flat-out idiotic, that it draws both blowback and ridicule from those kicked in the *** repeatedly about using such terms.
Political correctness attempts to address the issues I mentioned previously also in that it understands that our grasp of the differences and subtleties of other societies, religions, and races is imperfect, biased, and wrong. However, it attempts to apply a correction without comprehending that those to whom the correction is being applied will not instantly understand the subtleties involved. In addition, it tends to go too far. If a generalization that 'all Muslims are bad' is incorrect, the PC response can take the form of 'no Muslims are bad,' which is equally incorrect, even if somewhat closer to the truth; while risking outright rejection from the group that PC pressure is attempting to 'correct'.
And because such things tend to be applied to the minority by the self-appointed enlightened, any denigration of what is seen to be the majority is perfectly acceptable. Thus, one cannot insult or otherwise impugn Muslims; but Christians can be maligned without fear of offense by the enlightened in a society where Christianity is ubiquitous and not seen as an oppressed minority.
All this to say that it's perfectly natural. Obese people can be joked about and insulted; because so many of us are obese. It would be considered wrong to make fun of anorexics. One cannot tell jokes about Pollacks anymore in polite society; but one can make jokes about GOP members or Democrats. One cannot insult Muslims, but Christians are fair game.
And the fundamental mistake that all groups makes is assuming that the other groups want to be corrected.