What is the proper word or phrase to mean that group which is favored by the societal favoritism that civil rights movements generally try to remedy? In the United States I think the group would be male, white, heterosexual, Christian, and maybe a few other things (college educated, Northern, not disabled, cisgender, rich, not a juvenile, not a senior, and so forth). Where you draw the line is significant, but maybe it is enough to say that when some group of people who are demographically disfavored by society is talking together about their grievances, they know who their “them” is.
It obviously isn’t “majority” because male and white already eliminates most people.
In legal cases, the term suspect class is used to refer to groups of race, age, gender, etc. that might be subject of discrimination. What you want is the opposite of that. I suppose it could be called the non-suspect class, though that doesn’t seem to be very obviously clear. But then, many of the legal terms aren’t!