That's false. This narrative is from the Red Scare. It's propaganda actually.
China's system is meritocratic, which means it has more social mobility than any major countries on the planet.
You can't enter China's top universities with legacy or donation, and only by standardized exams. Backdoors do exist but only for members of the military, current high-ranking party members holding office and foreign students on diplomatic grounds, which do not count towards the quota.
Communism didn't kill anyone in the past, the stupidity of those in charge did.
No political system is inherently good or bad, let it be dictatorship or democracy. The devil is in the details, and how it's excuted. More often than not, it's human nature. All systems can be exploited, including the one we are in right now, right under our noises.