Yes, I host a lot of guests without profile pictures. At first I was squeamish, but as I've gotten experience I find that the communication via messaging tells me what I need to know. Many folks don't have photos they like but I always appreciate it! In addition if I really want to, once they book I look them up on Facebook because I'll have their full name by then. I know that if there is someone that I'm concerned about, I could contact Airbnb and work through rehoming them (never cancel the reservation yourself!). We've had great guests with profile pics of their cat, dog, or the woods.