The latest game on the left is called "check your privilege," and if you make any point about others perhaps less advantaged than you, you are given to understand that you cannot really comment objectively, given your advantage.
It’s quite an old game. Marxists used to call it "sociology of knowledge" , but the rules were similar. All of your opinions were alleged to be only the product of your class interest, and could therefore be discounted. If you advocated market economics and classical liberalism, for example, this was simply an expression of your class interest as a member of the bourgeoisie. It has the advantage that the intellectual content of your views can be ignored. Opponents do not have to argue with what you say; since it represents only your class interest it can be ignored. There is an exception. One group is sufficiently detached from the class system that their views have objective import. These are the Marxist intellectuals, of course.
The fallacies in "check your privilege" are straightforward and easy to identify, though Herbert Marcuse (remember him?)  would no doubt have dismissed them as part of "bourgeois logic." First is the argumentum ad hominem In which what is said is discounted, not because of any flaw or fault in its argument, but because of something pertaining to the arguer. It is not the substance or sense of what is said that is being criticized, but the status of the person putting it forward. The fallacy lies in the fact that the argument itself is not addressed, but irrelevant material is considered in its place.
The second fallacy is the genetic fallacy. Despite the name this has nothing to do with Darwin or Mendel, but involves a dislike of where an argument comes from. People are less inclined to accept views from those they dislike, whatever the merits of the actual views. The mistake is to suppose that the source of an argument affects its validity. A common meme is to assume that eventually someone will associate one side of an argument with Adolf Hitler, but it is still committed if you think that the views of rich white males can be discounted because of the three categories of those holding them.
Other fallacies are touched on, but all belong to the category of informal fallacies of relevance (intrusion), and represent considering that qualities pertaining to the arguer somehow undermine and diminish the argument. They don't. In its latest form it is simply an anti-intellectual way of doing down what the other side is saying without facing the difficulty of considering their argument.