I think that there are many misconceptions about the concept of gender queer. It has not been a particularly mainstream idea for very long. Arguably, it still is not mainstream.
Genderqueer is essentially a rejection of the binary gender system (male or female, boy or girl, man or woman). Claiming gender queer is basically saying, fuck a binary gender system, these gender roles that exist are too confining/limiting/inaccurate/fucked up etc.
Claiming genderqueer is not the same thing as saying you are trans. There is definitely overlap. Many radical trans people will also identify as genderqueer because they see the gender binary system as inherently oppressive. Some genderqueer people choose that identity because they see more than 2 genders. Others, because they don’t feel comfortable as either of the 2 genders. There are many reasons people choose genderqueer. It is a fairly fluid concept, with the main point of unity being a rejection of the binary gender system.
Claiming genderqueer is not oppressive. Claiming genderqueer does not cancel out other privileges that one may have. It is not a way to deflect those privileges. If a male bodied person says they are genderqueer, but they frequently pass as male, they still ought to acknowledge the way that male privilege plays a role in their lives. If a white person is genderqueer, that does not in any way eliminate their white skin privilege. And I have never personally encountered anyone trying to use genderqueer as a way of avoiding accountability for their other privileges.
The binary gender system IS oppressive. It is a means to attempt to regulate the behavior and lives of people based on their assigned gender. The binary gender system hurts many people on a daily basis- from people crammed into gender roles they do not fit, to people who are harassed, physically assaulted, and murdered because they do not fit into the gender binary.
I think it is fair to say that when non-queer people attack genderqueer, calling it oppressive, they are on the verge of queer bashing. It is not the place of straight, gender binary accepting people to tell others if their gender preference is or is not oppressive. And if calling a genderqueer identity oppressive is just a thinly veiled personal attack, then it is still extremely fucked up and problematic that the straight person has latched onto the queerness or genderqueerness as a point of attack.
Fuck the gender binary and fuck passive aggressive bullshit. I identify as genderqueer. I have never fit neatly into one of the 2 gender options anyways, and I wholeheartedly reject the gender binary system. I still have skin and class privilege, and identifying as genderqueer has nothing to do with those. The more people who identify as genderqueer the more potential space there is for people to experiment and play around with their gender identities and expressions. Thats not oppressive, in fact, it is liberating.
More information on genderqueer for folks interested in educating themselves.