What if most people didn't believe space and time were related?

I believe, as result of Einstein's Theory of Relativity, and its support by the Physics community, most people currently do. That's why virtually everyone thinks light speed is an absolute limit. I would suggest that the evidence supporting Relativity Theory is, actually, somewhat less than overwhelming. We have particle accelerator physics experiments in laboratories that could be artifactual results of the structure of the particle accelerators themselves. And we have some consistency between GPS calculations and Relativity, although GPS is actually done empirically. Some other astrophysical effects may have microeffects that can be seen as consistent with Relativity Theory. Of course, to take bit of a tangent, parapsychologists consistently find overwhelmingly statistically significant psychokinetic microeffects on automated coin tossing -- say, 50.001% heads vs. 49.999% tails, over a million trials, where experimental subjects were trying, psychokinetically, to achieve the result "heads". Does this convince you that we all have psychokinetic powers? It doesn't convince me. So, let's suppose that most people didn't believe that space and time were related. What would be the practical implications of such a change in people's beliefs? I think I can see one. Given our knowledge of earth-like planets in solar systems near our own, I believe -- given no faith in a light speed limit -- we would be making nuclear powered spacecraft a much greater priority, for purposes of interstellar travel. On the assumption that simple Newtonian mechanics would apply. We would simply reach the speed of light, and, then go faster. Perhaps, to five or ten times the speed of light. And go on to colonize these new Earths.