The quick is answer is “no.” There are many factors that directly affect your car insurance rate -- car make, model, your driving record, marital status -- and car color is simply not one of them.
The only caveat here is that the some people who prefer red cars are also the type of people who like to drive quickly. They are also generally the type of folks who are single, without any dependents. And of course childless drivers who like to move quickly are, on average, more prone to getting into car accidents, and therefore more risky to insurers.
That said, we’re lucky that car insurance carriers are like good law school students and don’t mistake correlation for causation. We get the benefit of the doubt, at the start. So go ahead and get whichever color car you like; your car insurance premiums will not be affected.
Nevertheless if you do buy a red car, be sure to drive safely.