Define "negative effects."
I'll say that there were zero negative effects. MacArthur was a legend in his own mind who should have been left in Bataan for the Japanese in 1941.
First, in the weeks leading up to the start of the Korean War, there were rumors of North Korean military movement. These rumors were passed along up the chain through the Korean Military Advisory Group (KMAG), the only US forces in Korea at the time, which MacArthur dismissed. He did not care about Korea and he didn't want to hear about Korea.
Second, when the war began, the US forces in Japan were in zero shape for fighting. They did not have the latest weapons, notably bazookas. Task Force Smith went to Korea armed with the 2.36 inch M9 Bazooka which was totally and completely useless against the Soviet T-34 tanks that the North Koreans had. If they had been armed instead with the M20, 3.5 inch bazooka, they might have been able to stop the North Korean column at Suwon, 30 miles south of Seoul, instead of Daegu, 150 miles south of Seoul.
Besides weapons, the men themselves were not combat ready. After World War II ended, most of the soldiers went home. The draft was still in effect and the occupation forces became a place to cycle recruits in and out. They did not train effectively and they were in no shape to fight a war. Furthermore, US forces that were initially sent to Korea were undermanned by 10-20%. By the time the Pusan Perimeter was established, the North Koreans had swept across all of the peninsula, they had crushed the ROK military, the defense line was barely holding and it was being plugged with inexperienced, poorly trained, under armed soldiers who were low on ammunition. US forces had been crushed at Suwon (Task Force Smith), routed at Daejeon (where General Dean was captured), and were on the verge of being pushed off the peninsula. All under MacArthur's watch.
Of course, MacArthur had the Inchon landing, a daring feat that defied all odds - the tides at Inchon has one of the largest high/low falls in the world, literally miles of mudflats at low tide where a ship would be stuck for 12 hours, and anyone trying to walk over it would be sucked into the mire. But after shelling the area and landing in three places, Inchon was secured in short order. Operation Chromite was an unqualified success.
However, rather than go around Seoul and cut off any more retreating North Koreans, US forces spent two weeks retaking the city, costing many lives and allowing the remaining North Korean forces to retreat east of the city. At the same time, MacArthur ordered ANOTHER amphibious landing at Wonsan, on the east coast. This time, however, the harbor was mined and the North Koreans were able to fire at boats from the shore. By the time the mines were cleared (5 days AFTER marines arrived on transports), the North Koreans had left Wonsan, and American and British soldiers had arrived by land, making the landing unnecessary.
This was the beginning of the end for MacArthur. The Chinese had been saying for quite some time that they would get involved in the war if UN forces crossed the 38th parallel. MacArthur ignored this because he WANTED the Chinese to get involved, because he WANTED a war with China because he WANTED to crush communism, send a message to the USSR, and to help his friend, Chiang Kei-shek and the ROC retake the mainland. MacArthur's push to Pyongyang was bad enough, but going to the Chinese border was suicidal and, between Chosin Resevoir, Kunuri and the Gauntlet, a couple thousand UN men needlessly lost their lives.
After the Chinese intervention, UN forces were pushed south of Seoul again, causing a third and fourth battle for the city. MacArthur was fired in April of 1951, being replaced with General Matthew Ridgeway (who had taken over for General Walker, who was killed in a car accident in December 1950).
Ridgeway was systematic and aggressive. He replaced commanders who had been fighting for the past six months with fresh people, people who were not satisfied with being defensive, folks who wanted to take the fight to the Chinese. Under Ridgeway, UN Forces commenced Operations Thunderbolt, Killer, Ripper, Courageous, Tomahawk, Rugged, and Dauntless (among others), pushing Chinese Communist forces back into North Korea, destroying any that remained in the South, and establishing a front line that remained virtually unchanged until the end of the war.
I can think of no downside to MacArthur getting sacked. His narrow-minded focus on Japanese reconstruction allowed his forces to become soft. At the same time, North Korean volunteers were fighting in the Chinese Civil War. When Kim Il-sung started the war, he had an army of well-trained veterans; MacArthur had guys sitting on the beach in Okinawa. Fortunately, the scrambling he did do worked and South Korea did not fall, but when opportunities to end the war presented themselves - namely blocking the escape of the bulk of the North Korean army from the South and stopping at the 38th - he didn't seize the opportunities. After capturing Pyongyang, rather than re supply his army with things such as food, ammunition, and winter clothing, he stretched his lines to the Yalu, allowing the Chinese to cut off and destroy whole divisions of his forces.
The US had technology and money on their side, the Chinese had numbers. If MacArthur had been given carte blanche to continue the war, would their have been a positive outcome? The use of nuclear weapons? Expanding the war to China? Overthrowing the Communist regime and replacing it with the ROC? I don't know, but in my mind, there was no downside to replacing MacArthur with Ridgeway.
As a rebuttal, here are a slew of US citizens who, for the most part, disagreed with Truman for firing MacArthur. Another woman wrote this letter, not only criticizing Truman for firing MacArthur, but saying that he was kow-towing to the communists and "socialist England." The UK lost the third most troops, behind South Korea, and the US.
TLDR - there was no downside. MacArthur allowed the North Koreans to get the drop on the South and the US. He did what he wanted to do, ignored his superior (Truman), ignored the warnings from the Chinese, and extended the war longer than necessary. Ridgeway was able to regain lost territory and hold the communist forces until an armistice was signed.