Mayor Rob Rue tells TMZ ... the arrival of 20,000 Haitian immigrants in the past few years in a town of 58,000 is straining infrastructure and causing a culture clash ... namely, an uptick in bad drivers and deadly car accidents.

The town's mayor says residents' pets are safe, but Springfield is seeing an increase in reckless driving incidents ... which Rue attributes to more Haitian immigrants behind the wheel.

Mayor Rue says the migrants aren't used to driving cars and aren't accustomed to the rules of the road in the United States ... and he says this is causing car accidents, harm, and sometimes death.

Trump pushed the debunked pet-eating conspiracy at this week's debate, and now the town's police force is being flooded with calls from concerned citizens from across the country ... asking if Trump's claims are true. As we told you, the cops are getting so many calls they can't do their jobs.

Mayor Rue says the fearmongering and misinformation are causing inefficiencies in Springfield's government ... and they "need help, not hate."

Some residents keep pushing Trump's conspiracy at city council meetings -- the videos are going viral -- but Mayor Rue says it's a mix of truth, conspiracy and lies.

There's an interesting tug-of-war going on here ... Mayor Rue says, "When we try to tell truth -- whether it's on social media or whether it's in meetings -- it's called a lie, but when someone else speaks it or posts it, it's called truth."

The mayor says the car accidents caused by migrants are "very serious" and he's not minimizing the real effects immigration is causing in town ... but he says Springfield doesn't deserve a negative national spotlight because of a baseless pet-eating conspiracy theory amplified by a presidential candidate.

Instead, Mayor Rue says Springfield needs "people to speak truth about our town, our community.”