It seems like several different things are getting intertwined here and people are arguing past each other based on perceived "sides" and largely imagined positions being projected onto one another.
You can have gender equality and feminism without casual sex. Many young people today, both male and female, feel like the current system they're embedded in is frustrating and unfulfilling.
Everyone's personal preferences are equally valid. We should accept that people who express unease or unhappiness with the current dominant cultural norms pressed upon them have legitimate feelings, rather than attack and insult them by suggesting their desires belong in "the 19th century".