Suppose the Universe was non-relativistic so time and space would be independent of each other. In other words, both of them separately would be absolute and independent of an observer's motion (unlike the absolute spacetime in relativity).
Above that, let's suppose the speed of light is infinite. Would the kind of cause and effect that we experience in our real Universe be the same in this imaginary Universe?
In our Universe, it takes time for a cause to propagate and have an effect at a distance from the cause. I assume the cause is transferred by e.m. radiation and ignore the other three forces. In case of the weak force the cause will propagate with a finite speed, but because I believe the weak force is not a fundamental force, but a residue force of a more fundamental force, namely the hyper color force transmitted by hyper gluons as is explained by Haim Harari in his Rishon Model (just as the strong force was once thought to be transmitted by massive pions which turned out to be wrong; the force transmitted by the pions was a residue force of the fundamental color force transmitted by massless gluons, but that aside).
So I think all causes in the sketched imaginary Universe are transmitted with infinite speed. Does this mean that everything in the Universe causes (simultaneous) effects on everything in the Universe? Of course, you can wonder how it can be that an effect anywhere in this Universe occurs simultaneously with a cause anywhere else [which seems to imply that they are the same, while in fact, they are inseparable in the absolute time that walks at the same pace everywhere in this Universe (?)] but particles move in continuous trajectories, which according to me means that all processes follow the rule that the cause occurs prior to the effect.
But I think there is a problem here. The question remains what will happen if all particles cause a simultaneous effect on all other particles and this effect simultaneously backfires on all particles. What will happen, if anything happens at all?