I'm having the same problem. The first time it happened about a month and a half ago, I was in the middle of a paid training gig with a client and some little brats FaceTimed me over and over and over again. SEVENTEEN TIMES within a five minute period. I had to excuse myself from my training and have my client go take a break so I could answer the call and ask the kids politely to stop. That resulted in them doing it over and over again in retaliation.
I contacted Apple, and they told me there's nothing they can do, and that I have to report it to "local authorities." That did absolutely no good, because we don't know which of the idiots initiated the call.
Tonight, it happened again. This time it was a budding group of little Neo-nazi white supremacists (I'm not making this up) who immediately shared an image of the Nazi skull symbol with an "SS," and they started talking about Confederate flags and making really hateful and dangerous anti-semitic comments. I was nice, but told them never to contact me again.
At 12:49 a.m., I got another call. This time, two of the boys had changed their avatars to be different version of the Nazi skull and cross-bones, and the other had a red image with a large swastika. I told them I used to work at Apple and would report them, and also report them to the FBI, which only made them laugh. I tried recording the screen but only got the audio since I'm working on two monitors...it recorded the wrong one.
FaceTime on my Mac won't let me block the participants of these calls. And they're not showing up on my phone as a FaceTime call. I can painstakingly go through my phone and use the "block this caller" feature, but I have to transpose the numbers and emails from my computer to my phone. There is no easy way to fix this on my Mac.
I need help.