I agree that you should refrain from commenting on FB. If you feel it's appropriate, timing wise, you could personally reach out to the family, even by a card or email, to offer your support.
These happenings bring out the mean in people. Several years ago, my then- husband's niece was arrested for killing her baby. (I can barely type those words, I am still so horrified after all this time.) There was no FB page devoted to the crime, but I made the mistake of going online and finding the local news coverage, from the town 1200 miles away. The assumptions made in the comments section by complete strangers were so ugly I wanted to vomit. Evidently, according to the comments, every single member of our extended family was to blame for the death of this baby. Never mind that ex and this sister, (mother of Niece), were estranged, or that this sister had basically alienated all but a very few family members. (I could write a book...) My ex and I had never seen the baby, didn't even know his name, and the paper published a picture of him. He looked so much like my own son as a baby that I was stunned. Last I had seen our niece, she was a sweet, quirky, mixed up but basically loving kid, and now she was in jail awaiting trial for the most heinous crime a person can commit. So, I am learning all of this, and at the same time, reading the vile hate in the comments section. Big mistake.
You didn't ask for them, but, (((((hugs))))) I really do kind of know how you feel.