FFmpeg is mountains of extremely complex C code whose entire job is processing untrusted inputs.
Choosing to make such code network-enabled if you can't trust your inputs, I would recommend to sandbox if at all possible. Otherwise you are asking for trouble.
The usecase for something like this is when you control both sides, server & client. There is some basic HMAC auth built into each request.
> I would recommend to sandbox if at all possible.
Since the server is a standard binary that doesn't need any special permissions, you could create the most locked down user in your server that only has access to a limit set of files and the GPUs and it'll work just fine. This is encouraged.