When I was a young man my father managed to read "gay" behavior into almost everything I did, long before I was sexual in any sense. It frustrated me terribly, because I knew even then that being gay meant having sex with men, period, and that did not predict how I would throw a ball, choose clothing, select television shows or any of the other ridiculous things that were trotted out about me.
I am a lot older now, however, have a son of my own, and see things from a different angle. You see, I did turn out to be gay. (Bi, actually, but the distinction is purely academic in this case.) My father handled it badly, but I now realize that he was worried what that might mean for me and was trying in his own limited, small-town, narrow-minded way to convey to me his fears.
I'm sure not excusing him. I wish he had been able to help me through my tortured teens instead of making them worse. I wish he didn't automatically assume that being gay was a death sentence, one way or another. I wish a lot of things had come down differently about it all.
But deep down, I also know that his neuroses came from genuine love. They were filtered through a lot of weirdness, sure. If they hadn't been, perhaps he could have just said he wanted me to be happy but he hoped that I knew how to take care of myself and was careful. After almost twenty more years of not-quite-discussing it, I finally did come out to him. It took a long time, but in the end, he did essentially say exactly that.
I don't know what your parent's "talk" would consist of, but I doubt that underwear preferences are what is really on their mind. Being gay may not even be. May be that they have just come to understand, whatever set it off, that you are a sexual adult. There are inherent dangers in that which a good parent will want their child to avoid.
I can't tell you how much stupid stuff I say to my son because I can't quite find the words to say things right, but I love him nonetheless. Not for their sake, but for yours, I encourage you to give them a break.
Be firm, however, about your right to wear briefs. Boxers are for guys with small balls...