Horses head down the stretch of the 145th Kentucky Derby at Churchill Downs. (Jamie Squire/Getty Images)

On Sunday, as a wet weather system finished making its way across the country, NASCAR postponed its Cup Series race at Dover International Speedway. The system was producing too persistent a rain, track officials decided. It made the track too dangerous. So they waited a day to run the Gander RV 400, the first Monday NASCAR race in Delaware in more than a decade.

Twenty-four hours earlier, while that weather system soaked the Midwest, the head baseball coaches at Arkansas and Kentucky, preparing to play in Lexington, Ky., huddled as their teams warmed up for a 1 p.m. first pitch. The pair discussed the soggy field and forecast for more rain. They, too, opted to push their competition back a day.

But just an hour west of Lexington, in Louisville, where the 145th running of the Kentucky Derby was to take place late Saturday afternoon, officials at Churchill Downs considered no such thing. They never do. As their website boasts: “The race . . . has continuously produced ‘the most exciting two minutes in sports’; uninterrupted, even when coinciding with profound historical events like The Great Depression and World Wars I & II.” Or, as Churchill Downs media boss Darren Rogers told CNN in 2014 when torrential rain drenched the track, “Lightning or a washout of the track could potentially cause a delay, but a postponement would be highly unusual.”

It would, however, be prudent.

The most egregious error made Saturday at the Kentucky Derby wasn’t the video review that disqualified Maximum Security, the first horse to cross the finish line. It wasn’t the contact Maximum Security caused with others as he came out of his straight line off the final turn, prompting objections from competing jockeys and the subsequent review.

Instead, it was that the thoroughbreds, which the horse racing industry always claims to be trying to protect, were allowed to run at all in conditions deemed too dicey for competitions involving human competitors.

That decision-making, rooted in the arrogance of history, triggered all the controversy that left a long shot, Country House, wrapped in Derby roses, and Maximum Security’s connections perplexed and in protest.

Postponing the race a day until the clouds cleared and the track dried a bit would have reduced the possibility of slips and slides forcing any jockey to correct.

But we really don’t care about horses, no matter the iconic status we’ve elevated them to in North America. Episodically, we embrace a Seabiscuit or Secretariat when a Triple Crown threat emerges, or a Zenyatta, the mare who ripped off victory after victory during an unprecedented run of consecutive wins in the early 2000s. Generally, though, we ignore the whole lot.

To be sure, although one of the most well-known racetracks, Santa Anita Park in Southern California, briefly shut down earlier this year during a three-month stretch when 23 horses died, few people paid attention to the most likely cause: rain-soaked dirt. That should’ve been alarm enough entering Saturday’s race.

It doesn’t take more than horse sense to understand that galloping a score of 1,400-pound beasts around a dirt oval turned into a mud soup at 40 miles per hour is dangerous. And there is science to validate it, too.

A study from as far back as 1991, “Risk factors associated with injuries in thoroughbred horses,” published in Equine Veterinary Journal, found that “. . . track surface was also associated with the risk of severe injury.” It stated that horses racing on firm turf had a significantly lower risk of severe injury compared to those running on a track altered by the weather. Specifically, it pointed out that “horses raced at Belmont when it was muddy had a significantly increased risk compared to Aqueduct dirt.”

And since the tragic breakdown of Barbaro at the 2006 Preakness, studies showing synthetic tracks were safer than dirt persuaded many tracks to invest in alternative surfaces.

So officials at tracks around the country are well aware of the hazard of racing in sludge. When the Triple Crown or Breeders’ Cup isn’t in the balance, data collected by Equibase shows some tracks cancel races because of inclement weather and poor track conditions all the time.

They shouldn’t hesitate to do so for their biggest events, either. NASCAR didn’t in 2012, when it postponed its biggest race, the Daytona 500, for the first time because of rain.

That the Derby is a nationally televised kickoff of sorts for the horse racing season shouldn’t preclude the sport from doing the right thing. It should inspire it.

Why chance marring an event and the sport any more by ignoring Mother Nature as the Preakness did tragically in 2016 when two horses in races leading up to the main card suffered fatal injuries running in rain?

In the end, Derby officials weren’t afraid of their moment as some other sports seem to be of theirs. Imagine the NFL awarding the Saints a trip to the Super Bowl instead of the winner on the scoreboard, the Rams, because of the missed pass interference and helmet-to-helmet hit on a would-be Saints receiver that most likely would have delivered the conference championship for the Saints.

But the most important thing at every race should be the welfare of the animals, and not the coffers behind the betting windows or the fancily dressed who may have to re-arrange travel plans because of a rainout.

Kevin B. Blackistone, ESPN panelist and visiting professor at the Philip Merrill College of Journalism at the University of Maryland, writes sports commentary for The Post.