Exactly. Just like in any field of study. Mathematicians, scientists, and philosophers do the same thing when they explain something new. Using these examples, the word “trigonometry” didn’t exist until we needed to talk about/teach it but the principles were still real; there were atoms (though unnamed) before we called them “atoms.” Really, we have to come up with words for everything because we make language.
So trans* people existed before they were called trans*, just as cats existed before we called them cats. The phrases the OP and others mention that relate to gender and sexuality come, in part, from queer and women’s studies departments. Dismissing this terminology as tumblrcore is as absurd.
Privilege simply means “statistically more likely to…” (be elected to a certain office, get a certain job, etc. White people in America are statistically more likely to be wealthy than POC, for example. Men are more likely to be CEOs. This is because these groups if people are born, respectively, white and male. Neither is an insult! I benefit from white privilege and I neither feel insulted by that concept in any way nor does it make me feel guilty. I didn’t choose my race. I do get I choose how I vote and behave, and I need to consider the needs of others. That is just empathy, and it’s what separates the rest of us from psychopaths.
“Check your privilege” means “try to be aware of the fact that you are at an advantage in certain ways and others are disadvantaged.” I don’t find that offensive. I actively try to check my privilege.
One common response to this stuff is “well I’m a SWM and I have a hard life.” It’s certainly possible for a wealthy SWP to have a harder life than a gay woman of color with a disability born to a poor family. Maybe he has crippling depression and cannot function, so is unable to enjoy his wealth or even leave his bed before he overdoses intentionally at age 25, while she excels in school, earns a scholarship to college, lands a good enough job that she can comfortably support herself, falls in love, finds her life fulfilling, and lives to be 100. There are so many kinds of suffering and difficulty, and everyone has their own story. However, statistically real privilege is still real.
To anyone who feels upset about being privileged: no, you are not supposed to intentionally make things harder for yourself. No, it is not impossible for you to suffer. But being called white isn’t any more of an insult then being told you’re (your height here).
How to help level the playing field: BE A DECENT HUMAN BEING. Do not be hateful, be kind, and take personal responsibility for your actions. That’s all. If you’re being told to check your privilege regularly, it probably means you are regularly being an asshole.