Why is it a custom to wear white on the holiday of Tu B'Av? Where did this custom begin and does it only apply to women? Are there other restrictions or qualifications for wearing white on Tu B'Av?
SE. Thanks for the question!
I'd never heard of a contemporary custom, but if there is one, I'm almost certain of its source.
Mishna Taanit, end of Chapter 4:
אמר רבן שמעון בן גמליאל לא היו ימים טובים לישראל כחמשה עשר באב וכיוה"כ שבהן בנות ירושלים יוצאות בכלי לבן שאולין שלא לבייש את מי שאין לו כל הכלים טעונין טבילה ובנות ירושלים יוצאות וחולות בכרמים
Said Chief Rabbi Shimon son of Gamliel -- there were no holidays for the Jewish people like the 15th of Av and Yom Kippur. On those days, the daughters of Jerusalem would wear borrowed white dresses -- everyone would borrow someone else's dress, to not embarrass someone who didn't have one -- and dance in the vineyards ...
The Talmud continues that single men would go out there to meet a spouse.
It doesn't say exactly why white dresses, but based on the logic of "everyone would borrow not to embarrass those who didn't have", here's what I'd assume: dyes were often expensive in Talmudic era, so if you owned a blue dress that meant you were made of money. Now you had to borrow a blue dress from someone else, which would make for a really messy game of who's borrowing from whom ... so instead they told everyone to stick with white, so you couldn't tell socieconomic class just from looking at their dress. (And a rich girl and poor one could swap dresses and no one would know.) Furthermore the dresses had to be dunked in a mikvah in case they were ritually impure, and if everything's white you don't have to worry what's a stain and what's just the dye.
If I would extrapolate from the original source, then, I'd say the custom would be specifically for single women to wear white.