It is real. I can't talk for colleges in the US, where this seems most rampant, but I've had my own experiences with these kinds of people in Europe. This is why it's so frustrating to see so many Redditors claim that "SJWs" don't exist outside of tumblr and a few particular sub-reddits.
About 6 years ago I decided to enroll in a literature class, because I loved reading and I needed a few more points to graduate. Another reason was that since I grew up in the Caribbean, I never had many people that shared my interest for English literature. The class consisted mostly of women, and there were 3 guys including myself. One day the teacher brings up Gothic literature, and how female writers back then had to hide their true identities and whatnot. The topic, of course, welcomes the subject of modern feminism; "Have things *really** changed since then?"*
I was then asked if I thought women should become fire-fighters. My reply was that if she meets the same criteria as male firefighters, they definitely should. I then went on to say that what worried me most is that if I'm ever hypothetically stuck in a burning building, I'd want my rescuer, at least, to be able to lift and carry the weight of an average adult male. I was branded a sexist by most of my class-mates, and the teacher told me she was disappointed in me. It got worse, when a girl loudly said they shouldn't be so hard on me, because I came from a "macho culture". The class then proceeded to spend the next 25 minutes lecturing me on my culture, because they all know someone who's been there once on vacation once. It was humiliating.
This is why it irritates and annoys me so much, when the top upvoted comment is something like "I've never encountered these SJW types personally in my neck of the woods. Therefore, these people do not exist anywhere in the world and are nothing more than fodder for Reddit's anti-SJW circlejerk"*