Are straight pipes legal where you live? Might consider reporting them if it's truly debilitating/illegal.
I like fast cars and fast motorcycle, but I hate obnoxious ones. For any street/strip car there's no reason to eliminate the catalytic converter or mufflers. Because the sound is largely about the resonance of the pipe length you can have exceedingly fast cars producing lots of horsepower be reasonably quiet especially at idle and residential speeds.
I had a heavily modified trans it was very fast It was a street legal car that I also took to the track for racing. It did have some technically off-road parts like long tube headers and other things that provide performance but it still had catalytic converters and mufflers. Between idle and about 3,000 RPM it was only slightly louder than stock not obnoxious at all above 3,000 RPM usually in the 5,000 to 6,000 range it sounded like it had an open exhaust system due to the residence value of the exhaust piping.
So anyway your neighbor is a jerk just to be a jerk and I would begin to lodge complaints with the police until they send someone out there especially if they leave for work at the same time every day and pull them over. Same thing for those Harley-Davidson idiots that want to put on straight pipes.
In my state, motorcycles aren't subject to any regulation at all at the machine level. I walked in and registered my 70's two stroke yamaha in minutes.
In California their emission requirements are much stricter and it doesn't matter if your car is classic or not all factory emission systems must be present. Now if you have a non-California version of a car that you bring into California it needs to comply to the emissions of wherever it was built but if you have a California version of a car that would have been stripped of its air pump and other things those need to be restored in order to get street legal in California.
Don't confuse the testing requirements with the requirements of the federal and state law.
It depends, but the muffler is what mostly reduces the noise. The difference between an OEM cat and a removed cat isn't always that much in my experience.
Elmer's signature catchphrase is, "Shhh. Be vewy vewy quiet, I'm hunting wabbits"
It may be illegal in Mississippi but there's no state inspection or emissions testing to catch it. If I recall, there's a few other states that don't have inspection or emissions testing also.
Needless to say, I was not writing a letter of my compliments to his supervisor.
The problem is the modification of adding aftermarket off-road use only emissions equipment. Especially if it's obnoxious to the neighbors.