Speaking from personal experience, I would say the dress codes made a sudden fall between 1968 and 1972. I was in high school in 1970 when girls were finally allowed to wear slacks instead of skirts or dresses. No blue jeans yet; that would come the following year. I entered the University of Missouri in the fall of 1972 and realized I was walking midway between Woodstock and Haight-Ashbury in more ways than one. By contrast, I can return to the campus today for a football game and see students in far more fashionable and upscale dress, possibly because today’s (in-state) tuition assures a wealthier clientele ($9,000/yr today vs. $500 in 1972).
I do not see a correlation with birth control. The Pill was legalized in 50 states in 1965 and to all people regardless of marital status in 1972 (see Eisenstadt v. Baird). Even though lax dress codes results in more bodily exposure, I don’t judge that as their primary aspect.
We tend to forget the level of unnecessary formality of the pre-reform period (before late sixties). I heard a first hand story about a high school girl who was getting re-dressed for class after physical education class. The instructor caught her putting on a pink slip under her dress. She was sent home for a dress code violation, as all underwear had to be white in color. Dress codes even covered underwear, even though exposure of such would be indecent.
When the hippies made news, reporters born before 1930 quickly denounced them for drugs, promiscuity and vagrancy. In fact, their society-wide influence was on music, art and dress.