"Oppression olympics" is a derogatory expression used to describe the argument that group X has it worse than group Y. Oppression olympics is bad for several reasons:
1. When people want to argue that group Y has it better than group X, this often involves trying to minimize or ignore some of the problems faced by Y.
2. Oppression Olympics often obstructs discussing and solving smaller problems, as if larger problems were the only ones we should focus on.
3. Oppression Olympics often ignores or erases the diversity of experiences within X and Y. For some individuals in group X, the biggest problems they face might be similar to those faced by group Y.
Take, for example, a recent essay by Chris Stedman, Atheism is not the "new gay marriage" (via Friendly Atheist). Stedman complains about the constant comparisons between atheism and LGBT rights. Stedman is in part obstructing discussion of some atheist problems. For instance, how are we supposed to talk about atheists telling people about their atheism without an analogy to LGB "coming out". Are we to develop the concept of "atheist coming out" from the ground up, rather than building on the perfectly good work done by LGBT activists?
Stedman is also ignoring the diversity of experiences within the LGBT community. For instance, I'm lucky enough that I live in the San Francisco Bay Area, where I don't worry about hate crimes or housing discrimination. I worry more about weird reactions from relatives and friends, which is a problem shared by many atheists. A reductio ad absurdum of Stedman's argument is that I cannot analogize my experiences to those of LGBT people even though I am literally part of LGBT. Further reductio ad absurdum: LG people cannot compare themselves to B people, who can't compare themselves to T people, who can't compare themselves to trans people of color.
On the other hand, Chris Stedman makes many correct and valuable points. Despite the derogatory title, "Oppression Olympics" are in fact beneficial for several reasons:
1. If we never talk about it, people may tend to think group X and Y have similar difficulties, or similar levels of difficulty. This could lead to ignoring or erasing problems that are not shared between the two groups.
2. If we compare the situation of group Y to the past situation of group X, then this tends to imply that the problems faced by group X are over.
Anecdotally, some individual atheists seem unappreciative of many of the problems faced by LGBT people as a group. Sometimes, they only seem to be aware of a few LGBT issues, particularly the legal battles that get so much mainstream attention. Sometimes they seem to think that the battle for LGBT rights will be over in a few decades (the continuing struggle for racial justice argues that it would take much longer). Other times, it seems like atheists think LGBT issues will all but disappear when religion all but disappears.
What I'm trying to say here is that when people argue over the "oppression olympics", both sides are right, and both sides make valuable contributions to the discussion. It seems like the two sides are disagreeing with each other, but much of it is a sort of pathological disagreement.
It's sort of like... trading cards. When you buy trading cards, you often buy them in random booster packs. Sometimes you find a really cool card in your booster pack, and you become attached to it. Later, you argue with other people about how great this one card is, even if objectively speaking it isn't really any better than other cards you could have gotten.
Likewise, we get attached to arguments. Lots of people think about Oppression Olympics, and depending on individual context and chance, we each think up some particular point to make about it. We get attached to this one insight, and then we argue with other people that our insight is the best. When really there are multiple correct insights to be had on both sides.