How can a drawish opening be fashionable? dfan's answer to this question suggested the following. Why would a specific opening become popular as the method of choice to play for a draw? Wouldn't it be better to select an obscure out-of-fashion variation that leads to a draw? That way you always have the chance to catch your opponent unprepared and score an extra 1/2 point.
If I choose a well known drawish opening, it sends two messages to my opponent:


Offer me a draw and I'll accept it
If you play for a win, you'll just smash against my rocks.  If you try too hard, you'll lose.  If you don't, you'll probably just get a draw anyway.


Of course, some opponents won't care and will fight for the win while others will be more than ready to throw in the towel, especially if there's a rating difference in the opponent's favor.

This really only applies to master play.  Amateurs make enough mistakes that nothing is drawish, nothing is safe.