My reaction to Gamergate was to continue playing video games and to continue not reading 'Games Journalism' because I already knew it was payola garbage. As for your friends my suggestion would be to discuss other shared interests. It's possible - even common - for both 'sides' of an issue to be way off the mark.
So, first off, there are some very interesting bits of "Games Journalism" or even just mild-mannered industry publications (Gamasutra et al) who are still quite worth reading even despite the GamerGate nonsense.
Second and more importantly, it's now in some third or later phase where frankly things have extended quite beyond just games. Both friends spend a lot of time online reading blogs, reading essays, and basically being literate on digital culture. That being the case, avoiding the ripples and crazy of that whole fiasco is hard.
There's a fascinating de facto trial of the limits of free speech in the age of mass point-to-point communication, and if you just stick your head in the sand because of GG you're going to be missing a lot.
My opinion on the matter is that if someone can say the phrase "ethics in video game journalism" with a straight face, it's time to abandon the conversation...
