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It's a cliche - a bunch of D&D nerds sitting around the table dressed as their characters. I saw it pop up most recently on an episode of Married at First Sight, where one of the grooms is a D&D player.
But in forty four years of playing, I have never sat at a table with anyone playing in costume, and (with the possible exception of playing at a con, where someone was cosplaying, too) I have never even seen anyone playing D&D in costume.
So where does the idea come from, that we dress up to play?

Sometimes I have dressed up, but it's always for DMing. It's great for ambience. I have played in one game only where everyone dressed as their PC's. BEST GAME EVER!

I dressed all in black to DM the Castle Ravenloft module back in the late 80s. But I used to dress all in black a lot back in those days. And now.

As a DM, isn't it costumary that anyone whose character gets a Girdle of Femininity/Masculinity must roleplay the change, full with appropriate costume?

I think the only time I've been around a table with people who were dressed up would have been during Halloween games. And those costumes were seasonal, not necessarily related to someone's character in the game. It still didn't exactly hurt the atmosphere though.

I have had players and GMs show up with props though. Not a full outfit but maybe a pair of non-prescription glasses or something to suggest a style. Using props like this or maybe showing up once in an outfit that suggests the type of clothing style seen in the game are things I can see happening without much fuss. It's pretty rare though and most characters don't wear outfits that would be practical for their players to wear.