What is a non causal system?
You can make a non-causal system that 'predicts into the future by T seconds' causal, and thus realisable, by adding a delay of at least T seconds.

There are cases where it makes sense to think about non-causal filters, because other things being equal, you can usually design a 'better' non-causal filter than a causal one.

One case is in audio reconstruction filtering. It's trivial to make an exactly linear phase filter with a symmetric impulse response. It's difficult, and then only an approximation, to get linear phase with a causal filter. As the time delay required is small, and so not an issue for music reproduction, the digital signal processing chain invariably uses delayed non-causal filters. This becomes more interesting when low latency is required, for instance filtering in a hearing aid.

Another case is for acoustic geophysical prospecting, analysing sound reflections to determine rock strata. The data is available as recordings, so there is no need to limit oneself to causal filters.