They currently go out of their way to remove microarchitectural side channels. Yes, there's almost certainly others, but it's pretty clear that the end goal is to allow non root creation of bpf programs.
We've seen Spectre exploits through sandboxed Javascript. Unless you separated the eBPF VM address space from the kernel address space, I suspect you would have the exact same problems that browsers have had. But if you did put them in separate address spaces, then why bother with eBPF? You could run a normal userspace program.