Until the mid 1960's, most American men had their hair cut in barber shops, and most American women had their hair "done" or "styled" in beauty parlors.
At the height of the hippie era, when men let their hair grow long, some beauty salons starting treating the tresses of both genders, and proclaimed themselves to be "Unisex" salons, to welcome men.
While it was their intention to imply that they provided the same services for both males and females, the terminology was inaccurate. A unisex salon would be one that provided service for members of just one sex. A business that served both men and women should be considered bisexual... but a large neon sign that promoted bisexuality might not draw many customers.
Actually, there was at least one "we clip anyone" salon long before the hippie era. In 1861, Arthur's Tonsorial Parlour in Virginia City, Nevada provided service for short-haired women during the population boom caused by the Comstock Lode silver discovery. Virginia City was such a boomtown that for a long time it housed the only elevator to be found between California and Chicago.
Virginia City is one of the oldest cities in Nevada, and also one of the oldest west of the Mississippi River. It is one of the most famous boomtowns in the Old West as it virtually appeared overnight as a result of the silver discovery in 1859. At its peak, Virginia City had a population of nearly 30,000. When the Comstock Lode ended in 1898, the city's population declined sharply. Today, Virginia City is but a shadow of its former glory, with about 1,500 people.
Virginia City could be considered the birthplace of Mark Twain, because in 1863 Samuel Clemens, then a reporter on the local newspaper, first used his famous pen name. Virginia City is also known for being the nearest town to the Cartwright Ranch on the Bonanza television series. It is also the name and the setting of a 1940 Errol Flynn movie set during the civil war, and the place where Marty McFly, the lead character in the Back to the Future trilogy, was killed. (info from Wikipedia and other sources)