Effect of offensive speech online on grad student life
It's hard to answer without knowing the specifics of what they post. However, it could be very damaging if it comes out. There's a large amount of online mob mentality that has the potential to ruin anyone's life. It doesn't help that many news sites are more than happy to write a story about minor Internet drama, which often gets even more people to talk about it.

I can see two ways this could be damaging to your friend's graduate career: 


Professors will want to protect their own reputation and might avoid working with your friend if they're seen as provocative or "bad" by others. Being someone's graduate adviser is an important relationship and some people will avoid associating themselves with your friend.
Some students might avoid taking classes from someone they see as "unsafe" or antagonistic. If they complain, your friend might not be given any TA positions by the school.


Could it be damaging to their post-graduate career? Certainly. There are countless articles about people who made one mistake or had a joke take out of context and now find it hard to find a job. Take a look at this article about a girl who took a "funny" picture at the Tomb of the Unknown Soldier:


  Life was inundated with emails demanding their jobs, so Lindsey was called into work. But she wasn’t allowed inside the building. Her boss met her in the car park and told her to hand over her keys. “Literally overnight, everything I knew and loved was gone,” Lindsey said. And that’s when she fell into a depression, became an insomniac, and barely left home for a year.


One bad Facebook joke and she loses her job. You also have "Donglegate," Michael Richards, Justine Sacco, etc. The Internet is a scary place.

Or maybe your friend never gets caught or no one ever cares and it all turns out fine. Who knows?