Let’s go to the main point: people believe that putting a picture on their profile will ruin their chance if they unluckily fall on a recruiter with preventions: racist, fatphobic, ageist, cacophobic, validist or any other, they could be rejected. Maybe. But what do you think will happen if you don’t? There will be a time you will need to go to an interview. Do you think that if the recruiter has preventions, those will disappear between the time you sent an email and the interview? Or maybe your infinite charisma will disable these bad traits? Or maybe you will go to the interview wearing a paper bag on your head, sunglasses, and gloves so no one will see what you look like? If recruiters want to discriminate you, they will. So, in my opinion, it’s better to be discriminated as soon as the resume screening: you will not waste time and won’t place your expectations in the wrong company. Do you really want, anyway, work for a discriminating company?!
This said, if you had done a targeted search, you shall not be worrying about being discriminated, as you should have on your list only non-discriminating companies. The more accurate is your search, the less you risk engaging with wrong companies.
Beside, a picture will help recruiters recognizing you when you show up at the interview, as well as recognizing you on any Internet publication, which can be useful when you have a common name. It implies that you have to control your e-reputation, though…